Technical field
[0001]The present invention is a method of designing a rolled H-section steel, rolled H-shaped steel, and a method of manufacturing the rolled H-shaped steel.
This application claims priority based on Japanese Patent Application No. 2017-028465, filed in Japan on February 17, 2017, which is incorporated herein by reference.
BACKGROUND
[0002]For the purpose of providing a structural system in which the, with economic and reliable to deformably resistance to temporary load due to seismic or impact other severe temporary causes, etc. Patent Document 1 steel beam It discloses.
[0003]The steel beam disclosed in Patent Document 1, the use of multiple distributed region determined by one or more cavities arranged in the web of the support member comprising a steel beam, deformation capacity is enhanced. The voids, when it reaches the critical stress are those distributed region configuration as inelastically deformed size and shape to ensure that, machinery and electric wire or the like can pass through the cavity.
CITATION
Patent Document
[0004]Patent Document 1: Japanese Patent 2008-175056 JP
Summary of the Invention
Problems that the Invention is to Solve
[0005]Here, steel beam disclosed in Patent Document 1, since the space in the web of the support member comprising a steel beam is formed, for example, if the outer peripheral surface of the web is coated or painted, formed in the web it is void of minute only, it is possible to reduce the painting amount, the refractory coating amount or coating weight of the web.
[0006]However, steel beam disclosed in Patent Document 1, by voids is formed in the support member to be steel beam web, since the partial loss in the portion of the cavity in the web occurs, yield strength of the web and rigidity is reduced. Therefore, the steel beam disclosed in Patent Document 1, the web of the support member comprising a steel beam, local buckling, shear locus 屈又 is disadvantageously liable to occur a local destruction phenomenon due clip ring seat 屈等there were.
[0007]The present invention has been made in view of the above circumstances, local while suppressing breaking phenomenon or the like, coating or the cost of surface treatment such as painting can be reduced rolling H-shaped due to local buckling design method of steel, rolled H-shaped steel, and to provide a method for producing a rolled H-section steel of interest.
Means for Solving the Problems
[0008]The present invention, in order to solve the above problems, employs the following.
(1) Design method rolled H-shaped steel according to the first aspect of the present invention includes an upper flange and a lower flange, and a web connecting the upper flange and the lower flange and the upper flange, the lower flanges, and wherein there is provided a method of the outer peripheral surface of the web to design a rolled H-section steel that is surface treated, cross-sectional second around strong axis in circumferential length Lp in the cross-sectional shape when viewed along the timber axis in a cross section perpendicular the value obtained by dividing the next moment Ix and surface treated economics Ix / Lp, when the area of the cross section was S, the bottom flange with, from the top flange satisfy the following equation (35) to (38) below and the height dimension H is 700mm or more to, the top flange and the width W of each of the lower flange is not less 1/5 or more and 1/2 or less of the height H, the thickness tw of the web 3 There 9mm more and the mm or less, so that the top flange and the plate thickness tf of each of the bottom flange is at 12mm or 40mm or less, the height H, the width W, the thickness tw, and the plate thickness tf set to.
(2) In the aspect described in (1) above, may be configured as follows: the used as beams rolled H-shaped steel extending in the member axis and said material axis of the rolled H-shaped steel condition both ends of the direction is fixed, at an intermediate portion of the member axis, conditions lateral movement in the width direction of the rolled H-shaped steel is restrained, and the intermediate load is acting vital from above the top flange under conditions that effect the end load to both ends of the member axis, the following (12) to (16) elastically Lateral buckling moment M of the beam calculated from equation cr with, the Lateral buckling in the beam so as not to generate, the height H, the width W, setting the thickness tw, and the thickness tf.
However, V cr : shearing force acting on the end of the timber axis direction of the beam, W cr : intermediate load acting on the intermediate portion of the timber axis direction of the beam, beta and gamma: load V cr , W cr below by equation (1) and (2) coefficient determined from formula, l: beams wood axial length, E: Young's modulus, I: sectional secondary moment about the weak axis of the lower flange, G: shear modulus, J: San safe for torsional constants, d b : plate thickness center distance between the upper and lower flanges, y: from one end thereof in a timber axis direction of the reference beam to any point of the timber axis direction of the beam length, theta y : twist angle occurs in the beam by bending Lateral, theta ' y : theta y first derivative of, theta " y : theta y second differential of, a:. a parametric for integration
　(3) described above (2) in an embodiment of the full plastic moment Mp said elastic Lateral buckling moment M of the rolled H-shaped steel cr is the square root of the value obtained by dividing the .6 to be less than, the height H, the width W, the thickness tw, and may set the thickness tf.
[0009]
[Number 1]

[0010]
[Number 2]

[0011]
[Number 3]

[0012]
(4) rolled H-shaped steel according to the second aspect of the present invention, the upper flange and the lower flange; and a web connecting the upper flange and the lower flange; a rolled H-beam comprising, the top flange , the bottom flange, and the outer peripheral surface of the web is treated surfaces; height H from the top flange to the bottom flange is located at least 700 mm; the top flange and the width W of each of the lower flange the There 1/5 or more and 1/2 or less of the height H; thickness tw of the web be 9mm or 32mm or less; the top flange and the plate thickness tf of each of the lower flange with 12mm or 40mm or less There; a value obtained by dividing the second moment Ix of about strong axis in circumferential length Lp in the cross-sectional shape when viewed along the timber axis in the cross section perpendicular to the surface treatment economics Ix / Lp, the When the area of ​​the surface shape and S, the height H, the width W, the thickness tw, and the thickness tf satisfies the equation (35) to (38) below.
[0013]
(5) Third production method of the rolled H-shaped steel according to aspects of the present invention, the above (1) to (3) the height is set by the design method of the rolled H-shaped steel according to any one of dimensioned H, the width W, to produce the rolled H-shaped steel of the thickness tw, and the thickness tf.
Effect of the invention
[0014]
　According to the above aspect of the present invention, while suppressing local breakdown phenomenon due local buckling, thereby reducing the cost of surface treatment such as coating or painting.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015]
FIG. 1 is a perspective view showing a rolled H-shaped steel according to an embodiment of the present invention.
[FIG 2A] is a front view showing the rolled H-shaped steel.
[FIG 2B] is a side view showing the rolled H-shaped steel.
FIG. 3 is an enlarged front view showing a surface treatment economics of the rolled H-shaped steel.
[Figure 4] and the surface treatment economics Ix / Lp of the conventional H-beam is a graph showing the relationship between the H / S.
In [5] a conventional H-shaped steel, a graph showing that the surface treatment economics Ix / Lp, the relationship between the H / S becomes "Ix / Lp <730 · exp ( -45 · H / S) " it is.
In [6] rolled H-shaped steel according to an embodiment of the present invention, a surface treatment economics Ix / Lp, the relationship between the H / S is "Ix / Lp ≧ 730 · exp ( -45 · H / S) is a graph showing that the ".
In [7] the rolled H-shaped steel is a graph showing that the relationship between the cross-sectional area S and height H becomes "0.015 ≦ H / S ≦ 0.065".
[Figure 8A] is a front view of the beam with the rolled H-shaped steel, both end portions are fixed lateral movement is a diagram showing a state of being restrained.
It is a side view of the state shown in FIG 8B] Figure 8A.
[FIG 9A] is a side view showing an example of a virtual displacement of the beam with the rolled H-shaped steel.
Is a bottom view showing a virtual displacement of the beam shown in FIG. 9B] Figure 9A.
It is A-A'line sectional view of FIG 9C] FIG 9A.
[10] and the conventional design method, in the design method of the present invention, is a graph comparing the shape of the beam, a transition of steel weights and possess performance.
In Beams rolled H-shaped steel is used according to an embodiment of FIG. 11A] The present invention is a schematic side view showing the equivalent bending moment when the intermediate load is bent like.
In FIG 11B] the rolled H-shaped steel is used the beam is a schematic side view showing an example of such antisymmetric moment when the intermediate load does not equal bending.
In FIG 11C] the rolled H-shaped steel is used the beam is a schematic side view showing another example of such antisymmetric moment when the intermediate load does not equal bending.
In FIG. 11D] the rolled H-shaped steel is used the beam is a schematic side view showing another example of such antisymmetric moment when the intermediate load does not equal bending.
In FIG 12A] the rolled H-shaped steel is used beam, theta is approximated by a predetermined series y is a graph showing the calculation results using.
In FIG 12B] the rolled H-shaped steel is used beam, theta is approximated by Fourier series y is a graph showing the calculation results using.
13 is a schematic side view showing the moment gradients used for evaluation of Examples of the rolled H-shaped steel.
[14] below (35) to (38) of various reduction H-beams satisfying equation (invention example) is a graph showing a conventional rolling H-section steel that does not meet these expressions.
DESCRIPTION OF THE INVENTION
[0016]
　Hereinafter, with reference to the drawings, it rolled H-shaped steel 1 according to an embodiment of the present invention (hereinafter, simply referred to as "H-shaped steel 1") will be described. Incidentally, omitted in the present specification and drawings, are denoted by the same reference numerals to constituent elements having substantially the same functional configurations, and their redundant description.
[0017]
　H-shaped steel 1, as shown in FIG. 1, mainly, housing, schools, offices, hospitals, low-rise buildings, high-rise building or in a building such as a skyscraper,, floor structure, dirt floor structure, or skeleton the structural material of the structure, and the like.
　H-beams 1 are hot rolled rolled H-shaped steel which is formed from a single steel plate by such (roll H-section steel). That is, in the H-shaped steel 1, the upper flange 21, lower flange 22, and web 23 are formed integrally.
Incidentally, built H-beams fabricated by welding a plurality of steel plates (upper flange 21, lower flange 22, and the web 23 is manufactured as the separate steel plate, built H-beams to which they are welded together) in the case where fatigue cracks due to repetitive force acting on the welded portion occurs, or when the welding assembly accuracy of H-shaped steel is poor, there is a possibility that applied accuracy of design method is reduced. On the other hand, in the case of rolled H-shaped steel, (since there are no junction) flange and web because it together, the generation of fatigue cracks is not assumed, and since a high dimensional accuracy, the application of the design method accuracy is maintained at a high level. From this point of view, the present invention is directed to a rolled H-section steel.
[0018]
　H-beams 1, for example, as a steel beam in buildings, used as a beam 2 extending in the wood axis direction Y (longitudinal direction of the H-beam 1). H-beams 1, as shown in FIGS. 2A and 2B, (cross-sectional shape of the section perpendicular to the timber axis direction Y) cross-sectional shape when viewed in cross section perpendicular to the wood axis direction Y is substantially H-shaped includes an upper flange 21 and lower flange 22 extending in the width direction X, and a web 23 extending in the height direction Z.
[0019]
　H-beams 1, as shown in FIG. 2A, with the upper flange 21 and lower flange 22 are upper and lower are provided, these upper flange 21 and lower flange 22 of the web 23 are linked. That is, in the H-shaped steel 1, substantially in the center in the width direction X of the upper flange 21 and lower flange 22 facing each other, the upper and lower ends of the webs 23 are connected.
[0020]
　H-beams 1, as shown in FIG. 2B, the entire extend in wood axis Y, having a predetermined length l. Then, H-shaped steel 1, the distance in the height direction Z from the plate thickness of the center of the upper flange 21 to the thickness of the center of the lower flange 22, between the thickness center of the upper flange 21 and the lower flange 22 a distance d b a.
[0021]
　Note that the distance d between the thickness center b is the distance in the height direction Z from the upper surface of the upper flange 21 to the upper surface of the lower flange 22, or from the lower surface of the upper flange 21 and the lower surface of the lower flange 22 in the height direction Z and the distance may be treated as approximately the same. Further, the thickness center distance d b is the distance in the height direction Z from the lower surface of the upper flange 21 to the upper surface of the lower flange 22, or the overall height H of the H-shaped steel 1, as substantially the same It can also be handled.
[0022]
　H-beams 1, as shown in FIG. 3, and the upper flange 21 and lower flange 22 are formed to extend in the width direction X, are formed extending webs 23 in the height direction Z. H-beams 1, centroid and strong axis extending (that section first moment becomes zero (center of gravity) with respect to any axis passing through the point) to the street and the width direction X, through the centroid and the height direction Z with two of the principal axes of the weak axis extending. The second moment about the strong axis is defined as Ix, the second moment around the weak axis is defined as Iy.
[0023]
　In H-shaped steel 1, the upper flange 21, the outer peripheral surface 20 of the lower flange 22 and web 23 (the surface of the H-beam 1), for example, application of a refractory coating material, only the winding or spraying, refractory paint or corrosion resistant coating coating, or surface treatment such as plating is performed. That is, in the H-beams 1, on the outer peripheral surface 20, the coating material, paint or plating the surface treatment material, such as, are provided. Incidentally, H-shaped steel 1, the upper flange 21, may have a surface treatment is performed to all of the outer peripheral surface 20 of the lower flange 22 and web 23, have a surface treatment is performed on the portion of the outer peripheral surface 20 it may be.
[0024]
　In H-shaped steel 1, in conjunction with the upper and lower surfaces 21a and left and right end surface 21b of the upper flange 21, and the upper and lower surfaces 22a and left and right end surface 22b of the lower flange 22, and left and right side surfaces 23a of the web 23, the sum of the cross-sectional shape extension, a circumferential length Lp in the cross-sectional shape of the upper flange 21, lower flange 22 and web 23. Then, H-shaped steel 1, when the outer peripheral length Lp increases, fireproof coating materials, (the amount of the surface treating material) paint or the amount of plating is increased.
Incidentally, in the H-beams 1 and the web and the flange are integrally molded, the junction between the web 23 and the upper flange 21 and lower flange 22 (4 locations) is curved connecting portion 23b called fillet is present . When calculating the circumferential length Lp may consider this fillet 23b (curved connecting portion). For example, the H-beams 1 represented by H1000 × W350 × tw12 × tf19, the one place of the fillet, the outer peripheral length Lp when the calculated assuming as 1 yen quarter of the radius of curvature 18mm is 3345Mm. On the other hand, the same H-shaped steel, if the fillet is not, i.e. no curved connecting portion, the outer peripheral length Lp assuming that web and flange is connected at a right angle is calculated to 3376Mm. Thus, differences in the two types of the outer peripheral length Lp which is calculated by the presence or absence of the fillet is about 1%, the effect of the presence or absence of fillet on the calculation results it can be seen that sufficiently small. The radius of curvature of the fillet, in the rolled H-section steel of interest, but is generally in the range of 12mm to about 20 mm, in the following description and by calculating the radius of curvature of the fillet as 18 mm.
Here, "H-shaped steel 1 represented by H1000 × W350 × tw12 × tf19" above, the height dimension H will be described later, the width dimension W, web thickness tw, and the flange thickness tf, respectively, 1000mm, 350mm, 12mm, the H-beams 1 is 19mm refers. The same applies to the following description.
[0025]
H-beams 1, (the distance in the height direction Z from the upper surface of the upper flange 21 and the lower surface of the lower flange 22) height H up to the lower flange 22 from the upper flange 21 is not less than 700 mm.
[0026]
H-beams 1, the distance in the width direction X between the left and right end surface 21b of the upper flange 21, and the distance in the width direction X between the left and right end surface 22b of the lower flange 22, respectively, the width of the top flange 21 W and the width W of the lower flange 22, these width W is 1/5 or more the height dimension H, is 1/2 or less.
[0027]
H-beams 1, each of the upper flange 21 and lower flange 22 (in the height direction Z, the distance between the upper and lower surfaces 21a or the distance between the upper and lower surfaces 22a,) predetermined thickness tf and having a web 23 having a predetermined thickness tw (distance between the left and right side surfaces 23a in the width direction X). Incidentally, the ratio of the thickness tf for thickness tw, and ItaAtsuhi tw / tf.
In H-beams 1, the thickness tw of the web 23 is at 9mm or 32mm or less, the thickness tf of the upper flange 21 and lower flange 22 is 12mm or more 40mm or less.
[0028]
Here, H-shaped steel 1 is, for example, when used as a beam 2 shown in FIG. 1, for suppressing the deflection of the height direction Z, are required to improve the flexural rigidity in the height direction Z. Then, H-shaped steel 1 (by extending the H-shaped steel in the height direction) by increasing the height H, since the second moment Ix of about strong axis is increased, the bending per unit weight to improve the rigidity, thereby improving the flexural rigidity in the height direction Z of the H-shaped steel 1.
[0029]
Also, H-shaped steel 1, the upper flange 21, the outer peripheral length Lp increases in cross-sectional shape of the lower flange 22 and web 23, the greater the surface area of the outer peripheral surface 20 which surface treatment such as coating is applied. In this case, fireproofing material, the greater the amount of the paint or plating the surface treatment material, the amount of work such as coating also by increased costs necessary for the surface treatment is increased.
Therefore, by reducing the surface area of the outer peripheral surface 20 by reducing the circumferential length Lp, it is required to reduce the surface treatment cost.
[0030]
Generally, for example, external dimensions constant H-shaped steel as defined in JIS G 3192 (H900 × W400 × tw19 × H -shaped steel represented by Tf28), the steel heavy per 1m is about 304kg / m, surface area per 1m is about 3.36M 2 is. For example, when the painting an outer peripheral surface of the outer Law constant H-beam with expensive refractory paint or chilling coating, the material unit price, for example 10,000 yen / m 2 becomes.
Therefore, if, when the unit price of the external dimensions constant H-section steel and 120,000 yen / ton, in the beam 2 of length 10m in wood axis Y, steel costs about 365,000 yen (120,000 yen / ton whereas the × 0.304ton / m × 10m), coating material costs approximately 336,000 yen (10,000 yen / m 2 × 3.36M 2 a / m × 10m). That is, by comparing the steel costs and coating material costs, due to the overall costs of such buildings, as well as steel heavy of H-beams 1, reducing the balance well the surface area of the outer peripheral surface 20 it can be seen that it is necessary.
[0031]
Therefore, the H-beams 1, index surface treatment economics Ix / Lp is a value obtained by dividing the second moment Ix of about strong axis in circumferential length Lp in the shape of a cross section perpendicular to wood axis Y to. When the surface treatment economics Ix / Lp is increased, since the second moment Ix of about strong axis relative to the outer peripheral length Lp becomes relatively large, while reducing the surface treatment cost, per unit weight flexural rigidity it is possible to improve the.
[0032]
Then, H-shaped steel 1 is based on the surface treatment economics Ix / Lp, height H described above, the width dimension W, web thickness tw, and the flange thickness tf is determined.
[0033]
H-beams 1, to have, as described above, surface treatment economics Ix / Lp height H is determined based on the width dimension W, web thickness tw, and a flange thickness tf, strong axis while increasing the second moment Ix around, it is possible to reduce the surface treatment cost.
[0034]
Specifically, as described above, the H-beams 1, the height H is greater than or equal to 700 mm, and 1/5 or more and 1/2 or less of the width dimension W is the height dimension H, of the web 23 thickness tw is a 9mm or more and 32mm or less, the thickness tf of the flange is 12mm or more and 40mm or less.
Furthermore, the cross-sectional area of when viewed cross-sectional area in the cross-sectional shape of the H-beams 1 and S a (H-shaped steel 1 in a cross section perpendicular to its wood axis direction Y, the upper flange 21, lower flange 22 and web 23 total and is referred to as S) of, H-shaped steel 1, in relation to the sectional area S and height H, above the surface treated economics Ix / Lp is, by the following (35) to (38) below to satisfy a defined relationship is. In other words, the H-beams 1, the height H, width W, thickness tw, and plate thickness tf satisfy the following (35) to (38) below. Thus, at the same time reduces the surface treatment cost, to improve the bending rigidity per unit weight, it is possible to suppress the excessive flexural deformation in the height direction Z in H-shaped steel 1.
[0035]
[Formula 4]

[0036]
Important performance indicators of H-shaped steel 1, bending the second moment Ix of about strong axis is structurally index governing the stiffness, the section modulus around strength is structurally index governing Bending Strength shaft Zx and , a steel weight is economical indicators (alpha sectional area S), is four circumferential length Lp which is also economical indicators. At this time, if exert second moment Ix of about big strong axis in the smallest possible circumferential length Lp, since it can be said that their high economic efficiency, in FIGS. 4-7, the longitudinal axis of the surface treatment economics Ix / Lp It is set to. Moreover, the section modulus Zx as a function of the second moment Ix and H-shaped steel 1 of the height H around strong axis, i.e., from being represented as Zx = Ix / (H / 2), high and utilizing the dimension H as a structural index, in FIGS. 4-7, and the H / S to the dimension H divided by the horizontal axis is economical index sectional area S.
[0037]
Here, the conventional H-shaped steel, in FIGS. 4 to 7, △ marks, ◇ sign, □ as each mark and ○ marks are shown existing standards all.
△ mark represents the "ASTM A6 / A6M-10a Annex A2 lists the dimensions of some shape profiles, ASTM International ," conventional H-section steel as shown in.
◇ indicia "BS 4-1Structural steel sections, Part1, British Standard, (2005) " which is a conventional H-section steel as shown in.
□ mark, "internal dimensions constant H-shaped steel, JIS Handbook Steel II, the Japanese Standards Association, (2015)" which is a conventional H-shaped steel as shown in.
○ mark is, "outside Law certain H-shaped steel, JIS Handbook Steel II, the Japanese Standards Association, (2015)" which is a conventional H-shaped steel as shown in.
[0038]
These conventional H-section steel, as shown in FIG. 5, in the above (35) to (37) below, within the scope of the k <6.1, is the envelope identifiable. That is, these conventional H-shaped steel, in based on the surface treatment economics Ix / Lp above (35) to (37) below, it was found that does not meet the k ≧ 6.1. In contrast, H-shaped steel 1 according to this embodiment, by considering the above-mentioned method of surface treatment economics Ix / Lp (35) to Expression (37) below, the structural indicators and economic indicators at the same time It can be taken into account.
[0039]
　Specifically, while suppressing the surface treatment cost even in the prior art, but is possible to increase the flexural rigidity was required, the conventional design method (design method does not use later in equation (12)), shown in FIG. 4 as such, it has not been possible to the k and 6.0 greater. The reason is that if you meet the above requirements, since the thus calculated lower than the actual value is design value of Lateral Buckling strength (earthquake resistance) and Lateral 屈補 Tsuyoshizai for not to lower the Lateral Buckling force It becomes necessary, because the economy is reduced. For example, k ≒ 6 (k <6) to become H-shaped steel targeting (H1100 × W300 × tw32 × tf40), seat 屈補 Tsuyoshicho Lb of when calculated by conventional design method described above, the H 4 .6 times (1100 × 4.6 = 5060) and small. That is, in the category of conventional design method, had to be installed Lateral 屈補 Tsuyoshizai every 5 m. Then, since the further Lb is within an amount of k ≧ 6.1 is in relatively small tendency tends to increase also the quantity of the seat 屈補 Tsuyoshizai. For this reason, in the prior art, were k <6.1.
[0040]
On the other hand, H-shaped steel 1 according to the present embodiment, in the above (35) to (37) below, by a k ≧ 6.1, can consider the structural indicators and economic indicators at the same time, the surface treatment cost at the same time reduced to a, it is possible to improve the bending rigidity per unit weight. Also, H-shaped steel 1 and, at the same time to reliably reduce the surface treatment cost, from the viewpoint of surely improving the flexural rigidity, as shown in FIG. 6, in the above (35) to (37) below, k ≧ it is desirable to 6.2 or k ≧ 6.25, it is more desirable that the k ≧ 6.3 or k ≧ 6.4.
[0041]
Also, H-shaped steel 1 is prevented vital avoid strength degradation due to the Lateral Buckling occurs, the viewpoint of avoiding a reduction in the energy absorbing performance at the time of an earthquake, and that twisting or wavy web during rolling from the viewpoint of the width dimension W of the H-beams 1 and sets 1/5 or more the height H, is set to k ≦ 8 in the above (35) to (37) below. For example, H1200 × W160 × tw7 × surface treatment economics Ix / Lp of H-beams 1 represented by tf16 relatively high, that is, the value of k in FIG. 5 is relatively large, but the k> 8 in the H-shaped steel 1, when calculated under the same conditions as example also be unable to obtain a sufficiently high bending strength (described later as was calculated based on the design method of the present invention described later, the seat屈補Tsuyoshi distance Lb is occurred Lateral buckling a shorter range than 15 times the length of H, the design strength relative to the total plastic moment Mp obtained by the product of the total plastic section modulus Zxp and steel F value of about strong axis the ratio is reduced to about 75%), there may not be enough earthquake resistance. Based on this study, it is an upper limit value of k ≦ 8.
For example, if the H1500 × W350 × tw19 × tf40, H1500 × W400 × tw22 × tf40, and H1500 × W500 × tw16 × H-section steel of Tf36, a k ≒ 8 (and k <8), as F = 345, When calculated in the same manner as in example to be described later, it can be confirmed that the seat屈補rigid spacing Lb does not occur Lateral buckling up more than 15 times the H (= 1500mm).
[0042]
In FIG. 6 illustrates enumerate examples of H-shaped steel 1 by the symbol ●.
Here, Example 1, the height H = 1150 mm, width W = 300 mm, web thickness tw = 32 mm, a flange thickness tf = 40 mm, fulfills the above-mentioned (35) - a (38) (H1150 × W300 × tw32 × tf40).
Example 2 has a height dimension H = 1100 mm, a width W = 280 mm, web thickness tw = 16 mm, the flange thickness tf = 30 mm, fulfill the above equation (35) ~ (38) (H1100 × W280 × tw16 × tf30).
Example 3, the height H = 1000 mm, width W = 250 mm, web thickness tw = 12 mm, a flange thickness tf = 16 mm, fulfills the above-mentioned (35) - a (38) (H 1000 × W250 × tw12 × tf16).
Example 4 has a height dimension H = 950 mm, width W = 250 mm, web thickness tw = 11 mm, a flange thickness tf = 25 mm, fulfill the above equation (35) ~ (38) (H950 × W250 × tw11 × tf25).
Example 5, the height H = 850 mm, width W = 200 mm, web thickness tw = 10 mm, a flange thickness tf = 16 mm, fulfill the above equation (35) ~ (37) (H850 × W200 × tw10 × tf16).
[0043]
Also, H-shaped steel 1, as shown in FIG. 7, in the above (35), and H / S ≧ 0.015, is also desirable to Ix / Lp ≧ 50. If the value of H / S is less than 0.015, for example, a flange thickness is to use a special ChokyokuAtsu H-beams exceeding 60 mm, available floor structure or the like of a building which is the application target present invention is is it is because it is difficult. Further, such a case, H is as small as 500mm or less, since the pillar applications of a building, out of the target of the present invention.
Furthermore, improved lower limit of Ix / Lp may be 35 for example, since Ix / Lp is surface treated economics Ix / Lp falls below 50 becomes too small, at the same time bending stiffness Reducing the surface treatment cost from the viewpoint of, the lower limit of Ix / Lp is preferably 50.
The upper limit of the H / S is preferably 0.065 (H / S ≦ 0.065), more preferably 0.060 (H / S ≦ 0.060) .
[0044]
Here, when reducing the surface treatment cost from the viewpoint of improving the bending stiffness at the same time, the height H may be increased (the H-shaped steel may you wait in the height direction) as described above. However, in the beam 2, that Fig. 8A, as shown in FIGS. 8B and 9A ~ Figure 9C,, the web 23 against the Plane of wood axis Y and the vertical direction Z out-of-plane deformation, Lateral buckling occurs. Then, under the conventional building codes Design of Beam 2 by (conventional design method), both end portions 2a of the beam 2 that horizontal load during an earthquake is applied, in 2a, or at an intermediate portion 2b of beam 2 in the portion moment of the negative bending occurs, it is necessary to sufficiently consider Lateral buckling that occurs the beam 2, can not be easily increased height H.
[0045]
Figure 10 is a graph of the calculation results shown in Table 1. I columns from column A of Table 1 shows a cross section specifications of the H-shaped steel. The cross-sectional area S in column A, the B column indicates the ratio of the cross-sectional area of the other H-beam to the cross-sectional area of a H-shaped steel having a basic performance comparison H900 × W400 × tw22 × tf40. The circumferential length Lp is the C column, the D column is the ratio of the outer peripheral length of the other H-beam to the perimeter Lp of H-beams to the base (H900 × W400 × tw22 × tf40 ). The second moment Ix around Tsuyojiku the E column, the F column indicates the ratio of the second moment of the other H-beam with respect to the second moment Ix of H-beams to the base. All plastic section modulus Zxp around Tsuyojiku the G column, the row H steel F value, the column I respectively show the full plastic moment Mp obtained by the product of the Zxp and F.
Here, since the value of the full plastic moment Mp is set the cross-sectional dimensions to be approximately the same, G column, the value of I column are substantially the same. Also, the J columns based on the design method of the present invention to be described later calculated design strength Mcn (calculated results based on the present invention), the K columns in all plastic moment Mp (Table 1 H900 × W400 × tw22 × tf40 is the ratio of the design strength Mcn of each H-beam this value for the definition and MPO), the L columns based on conventional design method calculated design strength Mcc (the prior art based on the calculation result), the M rows the ratio of the design strength Mcc of the H-beam to the total plastic moment MPO, respectively show.
[0046]
The conventional design method is based on calculation of the H-shaped cross-section shown in Steel limit state design criteria, the description of the Architectural Institute of Japan, is obtained by calculating the strength factor of 1.0.
On the other hand, the design method of the present invention, by replacing the following (12) to be described later derivation of the elastic Lateral Buckling moment shown in the book, which was calculated as 1.0 proof stress coefficient as in the conventional design method is there. Incidentally, when using the following equation (12) in the design method of the present invention, the beam (solid line) subjected to bending antisymmetric by horizontal load shown in FIG. 13, when acting superimposed vertical load (the dashed lines) target It is calculated as.
Also, a 20m each case seat屈補Tsuyoshicho is Lb, steel F value 325N / mm in either case 2 is set to.
[0047]
Here will be specifically described conventional design method described above. In the conventional design method described above, first, the cross-sectional shape of H-beams of interest, wood lengths, supporting conditions at both ends, and Yokoho Tsuyoshi presence or absence conditions around the weak axis of the H-shaped steel, which is calculated on the basis of the flexural rigidity, with torsional bending rigidity, San safe torsional stiffness, and Lateral 屈長 the like, to calculate the elastic Lateral buckling moment below (1.a) equation. Then, from the elastic Lateral Buckling moment and the full plastic moment of the H-beams of interest, it calculates the Lateral 屈細 length ratio. The value of the abscissa 屈細 length ratio, there are divided case of three ways depending on the magnitude relation between the elastic limit slenderness and plastic limit slenderness ratio described in the guidelines, in each case, Lateral 屈限 field strength of H-beams the calculation formula is defined. The Lateral 屈限 field strength is calculated by the nominal value of each element constituting the calculation formula, when assuming ultimate limit state, it is necessary to consider the variation of the member strength of interest, the engineering judgment introducing a tolerance factor is reliable index based, by multiplying this into the Lateral 屈限 field strength defines a Lateral 屈限 field strength in the ultimate limit state. Incidentally, according to the above guidelines, the strength coefficient is 1.0.
[0048]
[Formula 5]

[0049]
　In the above (1.a) type, EI Y : weak axis bending stiffness around, EI W : torsional bending rigidity, GJ: San safe torsional rigidity, k l b : Lateral屈長is, l b : Zaicho or LATERAL屈補Tsuyoshima length, C b : a moment coefficient.
[0050]
　Lateral屈長of k l b divided case for are as follows.
(A) both timber ends is rigidly joined to the columns, beams intermediate is not horizontal stiffening: k l b = 0.75 × l b
(b) one end of which is joined rigidly to the column, and the other end Lateral屈補section of the beam being transverse stiffening by Tsuyoshizai, the beam ends is horizontal stiffening by lATERAL屈補Tsuyoshizai section, and haze, the bending member such furring strip: k l b = 0.75 × l B
(C) simple beam: K L B = L B
[0051]
　Moment coefficient C b are as follows for the case classification of.
If (a) LATERAL屈補bending rigidity in a section moment varies linearly: below (1.b) formula
(b) if LATERAL屈補rigid intermediate bending moment in a section becomes maximum: C b = 1 .0
(c) simple beam without intermediate have Lateral屈補Tsuyoshi
　　fulcrum: (i) such distribution when load is applied: C b =
　　1.3 (ii) if the central concentrated load is applied: C b = 1.36
[0052]
[Number 6]

[0053]
M 　in the above (1.b) Formula 2 / M 1 represents a bending moment ratio of the wood ends or Lateral屈補Tsuyoshitan.
The Lateral屈細length ratio lambda b and the value of the elastic limit slenderness ratio e lambda b and plastic limit slenderness ratio p lambda b divided case of the magnitude relationship between, and, Lateral in each case屈限field strength M c (nominal yield strength) It is as follows.
(A) lambda b ≦ p lambda b　: M c =
M p (b) p lambda b E [lambda] B　: the note (1.d) the formula
[0054]
[Number 7]

[0055]
　Here, Lateral屈細length ratio lambda b is calculated by the following (1.e) equation. In the following (1.e) formula, M p : fully plastic moment F = y × Z p , F y : yield strength, Z p : a plastic section modulus.
[0056]
[Number 8]

[0057]
　Further, the elastic limit slenderness ratio e lambda b is 1 / √0.6. Plastic limit slenderness ratio p lambda b is case analysis as follows.
If (a) LATERAL屈補bending rigidity in a section moment varies linearly: below (1.f) formula
(b) if LATERAL屈補rigid intermediate bending moment in a section is maximized: p lambda b = 0.3
[0058]
　The Lateral屈限field strength M in ultimate limit state cr is obtained by the following (1.g) equation.
[0059]
[Number 9]

[0060]
　Compared to the conventional design method described above, the design method of the present invention, by replacing calculation formula of the elastic Lateral Buckling moment shown in the book (the above (1.a) below) in the following equation (12) below, Lateral屈細 length ratio and is obtained by calculating the Lateral 屈限 field strength. Incidentally, proof stress factor to account for ultimate limit state, was similar to the conventional design method 1.0.
[0061]
Shows four types of H-section steel and the horizontal axis of the graph shown in FIG. 10, the vertical axis, (the values shown in Table 1 B column) the ratio of the sectional area S, the ratio of the outer peripheral length (in column D of Table 1 value), the values shown in the column F of the cross-section ratio of the second moment (Table 1 around strong axis) values are shown in column K ratio (Table 1 design strength based on the design method of the present invention), and the conventional design shown the ratio of the design strength based on the law (the values shown in M columns of Table 1) are to be compared, respectively.
As shown in FIG. 10, under conventional design method, by increasing relatively the height H relative to the width W, the bending increases the rigidity (second moment Ix of about α strong axis) by also while it is possible to reduce the steel weight (alpha sectional area S), it is given by the product of bending strength (alpha "section modulus Zxp around strong axis" and "allowable bending stress of fc" " allowable bending strength ") it can be seen that there is a tendency to decrease. This section modulus Zx around strong axis, Zx = Ix / from being expressed as (H / 2), if Ix is the same, it tends to Zx When H becomes large decreases (Reason 1 a), allowable bending stress of fc, it is necessary to reduce considering the Lateral buckling that occurs the beam 2, the greater the height H is relatively, the Lateral buckling is likely to occur (reason 2) it is due.
[0062]
[Table 1]

[0063]
For the reasons 1, it may be able to alleviate the performance degradation by setting the height H and width W of the beam 2 to each other properly. In contrast, for the above reasons. 2, it can not be solved by simply setting the height H and width W of the beam 2 properly, preventing the reduction of the allowable bending stress of fc by Lateral Buckling of the beam 2 is the main technical challenge. As a method of preventing a reduction of the allowable bending stress of fc, the stiffening member for the bending Lateral provided on the beam 2, a method of reducing the seat 屈補 rigid spacing are also contemplated. However, the provision of a stiffening member on the beam 2, cost savings by reducing the surface treatment cost and the like becomes meaningless.
[0064]
H-beams 1, used as a beam 2 extending in the wood axis Y, as shown in FIGS. 8A and 8B, both end portions 2a of the timber axis direction Y of the beam 2, 2a are in rigid connections to the column 3, etc. It is fixed. In this case, both end portions 2a of the beam 2, 2a, for example, if the RHS or the like is used as a pillar 3, that is welded to the diaphragm 30 provided on a side surface of the square tube, the column 3 rigidly joined in the fixed support.
[0065]
Further, both end portions 2a, 2a of the beam 2, when the reinforced concrete column or unreinforced concrete column is used as a pillar 3 may be welded to the steel beam which is substantially orthogonal to each other within the pillar 3. Further, both end portions 2a, 2a of the beam 2, when the steel reinforced concrete column is used as a pillar 3 may be welded to steel columns extending in the height direction Z within the pillar 3.
[0066]
H-beams 1, both end portions 2a of the timber axis direction Y of the beam 2, 2a may be fixed in semirigid junction or pin junction pillar 3 or the like. Incidentally, as the semirigid bonding refers to bonding format restraining to some degree the rotational movement of the beam 2 with respect to the pillar 3, the bending stress can be transferred between the pillar 3 and the beam 2 is small compared to the complete rigid connections the say. Further, the pin junction, refers to a bonding form which does not restrain the rotational movement of the beam 2 with respect to the pillar 3, the bending stress can be transferred between the pillar 3 and the beam 2, it refers to a nil or minimum. The semirigid junction, the pin junction and rigid connections definitions shall conform to the European design standard (Eurocode3 Part1-8).
[0067]
Also, H-shaped steel 1, in the intermediate portion 2b of the timber axis direction Y of the beam 2, above the upper flange 21, floor slab 4 of the concrete and the like are provided. Floor slab 4 is, for example, concrete slabs were concrete main structure or deck synthetic slabs where the deck plate or the like made of concrete and steel and the main structure is used.
[0068]
Also, H-shaped steel 1, in the intermediate portion 2b of the timber axis direction Y of the beam 2, one or more shear connectors 25 such as headed studs are provided at predetermined intervals on the upper surface of the upper flange 21. Shear connector 25 from the upper surface of the upper flange 21 of the beam 2 is provided to protrude upward, it is buried such as concrete or the like of the floor slab 4 above the upper flange 21 of the beam 2. At this time, H-shaped steel 1, by being embedded like to one or more shear connectors 25 floor slabs 4, in the intermediate portion 2b of the timber axis direction Y of the beam 2, as shown in Figure 8A, the beam 2 lateral movement is restricted in the width direction X.
[0069]
Also, H-shaped steel 1 according to the present invention, as shown in FIG. 8B, the intermediate load due to the weight and live load, etc. of the floor slab 4 is applied. At this time, H-shaped steel 1, in the intermediate portion 2b of the timber axis direction Y of the beam 2, intermediate load, such as a uniformly distributed load from above acts on the upper flange 21, and each column 3 is tilted by an earthquake or the like case, both end portions 2a of the timber axis direction of the beam 2, the end load from the pillar 3 in 2a the act. Furthermore, H-shaped steel 1, both end portions 2a of the timber axis direction Y of the beam 2, in each of the 2a, bending moment and shear force acts.
[0070]
Under the design method of the present invention, as shown in FIG. 9A ~ Figure 9C, as the target the beam 2 extending in the wood axis Y, both end portions 2a of the timber axis direction Y of the beam 2, with 2a is fixed , in the intermediate portion 2b of the timber axis direction Y of the beam 2, the lateral movement of the width direction X of the beam 2 is restrained, the intermediate load is applied from above the upper flange 21, and both end portions of the timber axis direction of the beam 2 2a, under conditions that effect the end load 2a, the elastic Lateral buckling moment M of the beam 2 cr can be calculated with high accuracy.
[0071]
In Figure 9A ~ Figure 9C, using a local coordinate system X-Y-Z fixed in the left end portion 2a of the beam 2, the rotation of the beam 2 and the direction of travel of the left screw and positive. Further, in FIG. 9A ~ Figure 9C, solid lines represent free body of the beam 2, the broken line represents an example of a virtual displacement that occurs free body of the beam 2 by bending Lateral.
[0072]

upper flange 21 of the beam 2, the displacement in the X direction on the center line 0-0' (lateral movement) is assumed to be constrained. Geometrical boundary conditions of the end portion 2a of the beam 2 is defined by the terminal conditions of a power series that approximates the Lateral屈変type. Incidentally, the beams 2, as well as torsional bending occurs to the default rotation axis 0-0' by bending Lateral deflection occurs as a secondary for small deformation. In this analysis, dealing upper flange 21, a lower flange 22 and web 23 as a flat plate, the strength of the beam 2 against bending Lateral includes a bending stiffness in the plane of the upper flange 21 and lower flange 22, the upper flange 21, the lower It shall be governed by the torsional rigidity of the flange 22 and web 23.
[0073]

Vertical etc. distributed load W as an intermediate load on 0-0' at an intermediate portion 2b of beam 2 cr assumed that acts. Further, bending moment M on the right end portion 2a of the beam 2 cr and shear forces V cr acts, the left end portion 2a thereof and balances the bending moment M and shear force V of the beam 2 is assumed to act. In this case, M cr and V cr and W cr relationship with, from balance conditions of force, respectively, the following equation (1) can be expressed by equation (2).
[0074]
[Formula 10]

[0075]
Here, l is the length of the timber axis direction Y of the beam 2, y is one end thereof in a timber axis direction of the reference beam 2 (the case of those shown in FIG. 5, the left end portion 2a) from the beam 2 to any point of the wood axial length. The β and gamma, a coefficient determined by the load condition of the intermediate load, V from the analytical solution cr , W cr , M, to clear the V, elastic Lateral Buckling moment M cr is intended to represent a.
[0076]
Incidentally, illustrating the relationship between the beam 2 bending moment distribution and β and γ in FIG. 11A ~ FIG 11D. If the intermediate load is bent equal in wood axis direction Y of the beam 2 (symmetric buckling), as shown in FIG. 11A, the β zero. Also, if not in wood axis direction Y of the beam 2 the intermediate load is equal bending (asymmetric buckling), as shown in FIG. 11B ~ FIG 11D, the beta, 0 super 3 following real (Here, FIG. 11B ~ FIG. 11D, respectively, β = 1, β = 2, illustrates the case of beta = 3) to. Then, beta, gamma, the above (3a) formula, is determined by (3b) expression.
[0077]

to handle Lateral Buckling as linear buckling problem, Zaijiku direction coordinate values deformation of each part of the beam 2 by bending Lateral (i.e., wood axis of the beam 2 from the left end 2a of the beam 2 previously expressed as a continuous function of length) y to an arbitrary point in the direction. At this time, the torsion angle θ of the cross section that occurs on the beam 2 by bending Lateral y , as shown in FIGS. 9A ~ FIG 9C, it should be continuously smoothly in the timber axis Y.
[0078]
In the present invention, to derive an analytical solution of the elastic Lateral Buckling moment by series approximation deformation of each part of the beam 2 by bending Lateral. Since Lateral Buckling is not accompanied by distortion of the cross section of the beam 2, other variations necessary for derivation of analytical solutions, i.e. the deflection of the beam 2 shown in FIG. 9C [delta] z , rotation angle θ of the beam 2 shown in FIG. 9A x , and the rotation angle θ of the lower flange 22 shown in FIG. 9B z , respectively, can be expressed by the following equation (3) to (5) below. Thus, deformation of each part of the beam 2 by bending Lateral ([delta] z , theta x , theta z ) is, theta y can be represented uniquely by.
[0079]
[Number 11]

[0080]
Here, d b is the thickness center distance between the upper flange 21 and lower flange 22, y is the length of up to any point in the timber axis direction of the beam from one end to the timber axis direction of the reference beam . Shita ' Y is Shita Y represents the first derivative of. a is an auxiliary variable for the integration.
[0081]

when the beam 2 is flexion Lateral occurs, the total potential energy Π of the system is given by the following equation (6).
[0082]
[Number 12]

[0083]
Here, .DELTA.U the strain energy beam 2, [Delta] T is the potential energy of the external force.
[0084]
Then, .DELTA.U as the sum of the strain energy due to strain energy and pure torsion by torsional bending is given by the following equation (7).
[0085]
[Formula 13]

[0086]
Here, E is Young's modulus, I is the second moment about the weak axis (Z-axis) of the lower flange 22, G is the shear modulus, J is a torsion constant San safe. Shita ' Z is Shita Z represents the first derivative of.
[0087]
Next, [Delta] T is, M cr , V cr , and W cr as the sum of the potential energy is given by the following equation (8).
[0088]
[Number 14]

[0089]
Here, theta x (l) and [delta] z (l) , respectively, theta of the right end portion 2a of the beam 2 x and [delta] z represents an.
[0090]

any θ of material axial direction Y of the both end portions 2a, 2a is an acceptable fixed supported beam 2 y can be approximated with any accuracy by finite series.
[0091]
That is, the Fourier series expansion given by the following equation (9) can be applied to the majority of the continuous function, since the calculation of series is simple, history buckling studies by energy method, both Fourier series It approximates the buckling deformation by.
[0092]
[Number 15]

[0093]
In contrast, in the present invention, both end portions 2a of the beam 2, if 2a is fixed by rigid connections, both end portions 2a of the timber axis Y, 2a as the abscissa屈変shaped fixed supported beam 2, in particular, theta in series given by the following equation (10) y can be approximated to.
[0094]
[Number 16]

[0095]
Here, a n is the undetermined coefficients of the n items. If you solve the asymmetric buckling and 2 k.
When solving a symmetrical buckling and 1 to k, applying the above (10) to 1/2 of the portion of the length l of the beam 2.
[0096]

the principle of minimum potential energy, the following equation (11), by substituting equation (7) and (8), further substitutes the (1) to (5) it is, as a basic equation of the elastic Lateral buckling moment, obtained the following equation (12).
[0097]
[Formula 17]

[0098]
[Equation 18]

[0099]
Here, A, B, C and D are the following (13) theta shown in formula ~ (16) y is a functional of, for l in each formula disappears by integration, they theta y depends only It is a factor.
[0100]
[Number 19]

[0101]
Here, beta, gamma is loading condition is a prerequisite V cr , W cr above by (1) is a coefficient determined by equation (2). Then, l is wood axis Y length of the beam 2, E is Young's modulus, I is, the moment of inertia of area about the weak axis of the lower flange 22, G is the shear modulus, J is San torsional constant of safe, d b is the thickness center distance between the upper flange 21 and lower flange 22, y is from one end portion serving as a timber axis direction of the reference beam to any point of the timber axis beam length is the difference. theta y is a torsional angle generated in the beam 2 by bending Lateral. theta ' y is theta y first derivative of, theta " y is theta y .a representing the second derivative of an auxiliary variable for the integration.
[0102]
Incidentally, equation (12) is a linear sum of the resistance to strength and net twisting against twisting bending, is generally B ≠ A. Incidentally, the design method disclosed in Japanese Patent Application Laid-Open Publication No. 2016-23446, for the case of acts antisymmetric bending moment in the beam 2 which lateral movement is restricted in the upper flange 21, respectively different in the two Strength we propose an approximate solution of the precision of the elastic Lateral buckling moment gives a correction factor.
[0103]

theta by the above equation (9) or (10) of the series y for the case of approximating the obtained analytical solution of the elastic Lateral Buckling moment. Undetermined coefficient sequence (a n ) requirements to minimize equation (12) with respect to is determined from the following equation (17), we obtained the following equation (18) by performing these differential. Incidentally, f below (18) wherein nm is expressed by the following equation (19).
[0104]
[Number 20]

[0105]
[Number 21]

[0106]
　Here, the (19) L in formula nm , M nm , N nm , O nm is expressed by the following (20) to (23) below.
[0107]
[Equation 22]

[0108]
　Here, theta n is theta y represents the n-th basis function of a power series that approximates the. For example, for formula (10), the following equation (24). Incidentally, theta ' n and theta " n , respectively, theta n represents the first derivative and second derivative of.
[0109]
[Number 23]

[0110]

　above (17) is undetermined coefficients a 1 , a 2 , ..., a n when providing a value other than zero for at least one, the possibility of buckling occurs. Therefore, the (17) determinant of type of the coefficient matrix must be zero. That is, by solving the N-order equation below (25), can be obtained analytical solution of the elastic Lateral Buckling moment.
[0111]
[Number 24]

[0112]
　Further, theta by the third term partial sum of a power series in (9) or (10) y analytical solution of the elastic Lateral Buckling moment when approximating the is given by the following equations (26) - (33) .
[0113]
[Number 25]

[0114]
　In this case, the minimum positive value in the real solutions of the equation (26) becomes a first-order elastic Lateral Buckling moment of the beam 2. H-beams 1, used as a beam 2 extending in the wood axis Y, both end portions 2a of the timber axis direction Y, with 2a is fixed, at an intermediate portion 2b of the timber axis Y, the width direction of the beam 2 lateral movement of the X is bound, intermediate load acts from above the upper flange 21 and timber axis direction of the both end portions 2a of the beam 2, under conditions which effect the end load 2a, below (12) - (16) elastic Lateral buckling moment M of the beam 2, which is calculated from the equation cr basis, as is not generated Lateral buckling the beam 2, the upper limit of the surface treatment economics Ix / Lp is determined is preferred.
　In other words, as 1.0 yield strength coefficient as in the conventional design method described above, the design strength Mcn calculated by the design method of the present invention, within a range that does not significantly smaller than the full plastic moment Mp, more specifically, All plastic moment Mp below (12) to (16) elastically Lateral buckling moment M is calculated from the equation cr square root of the value obtained by dividing the 0.6 (√ (Mp / M cr a) ≦ 0.6) as described above, to determine the upper limit of the surface treatment economics Ix / Lp, this limit to be less than, the dimensions of the H-shaped steel 1 (height H, width W, web thickness tw, and the flange it is preferable to set the thickness tf). As an example of this case, determined for Mcn when the seat屈補Tsuyoshi interval Lb is 15 times the H, so as to satisfy the Mcn / Mp ≧ 0.95, the upper limit of the surface treatment economics Ix / Lp and the like to be.
[0115]
[Number 26]

[0116]
　Here, beta, gamma is loading condition is a prerequisite V cr , W cr below by equation (1) is a coefficient determined from the equation (2). Incidentally, V cr is the shear force acting on the end portion 2a of the timber axis direction Y of the beam 2, W cr is an intermediate load acting on the intermediate portion 2b of the timber axis direction Y of the beam 2.
　Further, l is wood axis Y length of the beam 2, E is Young's modulus, I is, the moment of inertia of area about the weak axis of the lower flange 22, G is the shear modulus, J is San torsional constant of safe, d b is the thickness center distance between the upper flange 21 and lower flange 22, y is from one end portion serving as a timber axis direction of the reference beam to any point of the timber axis beam length is the difference. theta y is a torsional angle generated in the beam 2 by bending Lateral. theta ' y is theta y first derivative of, theta " y is theta y .a representing the second derivative of an auxiliary variable for the integration.
[0117]
[Number 27]

[0118]
　Incidentally, the design method described above is preferably implemented by a computer device that executes a temporary program recorded on a tangible recording medium is not (not shown) by a CPU (not shown) (not shown). In this case, the computer device, in accordance with the instruction from the input device operated by the operator, and executes the design method described above, the dimensions (height H of the H-shaped steel 1, a width dimension W, web thickness tw, and may output the result of designing the flange thickness tf). The output design results is preferably visibly output via an output device (not shown).
[0119]
　Set design result by executing the design method described above: according to (dimensions height H, width W, web thickness tw, and flange thickness tf), the existing rolling technology, H-shaped steel 1 preferably it is produced. Thus, the dimensions defined by the above-described design method can (height H, width W, web thickness tw, and flange thickness tf) of H-shaped steel 1 of obtaining.
[0120]
　As shown in FIG. 10, under conventional design method, if simply increasing the height H of the beam 2, but can be improved flexural rigidity, Lateral Buckling force decreases bending strength of the beam 2 is lowered Therefore, it could not improved that combines bending stiffness and Lateral Buckling force of the beam 2.
[0121]
　In contrast, H-shaped steel 1 according to the present embodiment, under the design method of the present invention, the above (12) to (16) elastically Lateral Buckling moment M of the beam 2, which is calculated from the equation cr in based, the upper limit of the surface treatment economics Ix / Lp is determined. Therefore, H-shaped steel 1 is reduced cross-sectional area S of the beam 2 is at the same time improves the surface treatment economics Ix / Lp, it is possible to maintain the bending strength is high not only bending rigidity of the beam 2. Therefore, it is possible to improve by both bending stiffness and Lateral Buckling force of the beam 2.
[0122]
　Table 2, Examples 1-5, shows the comparison with the conventional design method in the design strength of the bending member becomes beam 2. Calculation of the design strength of the bent material made here, for the conventional design method, described above, based on the calculation of the H-shaped cross-section shown in Steel limit state design criteria, the description of the Architectural Institute of Japan, the strength factor of one. calculated as 0. The calculation of the embodiments based on the design method of the present invention replaces the derivation of the elastic Lateral Buckling moment shown in the book in equation (12), calculates the strength coefficient as in the conventional design method as 1.0 did.
Examples shown here, in order to compare with the conventional design method and design method of the present invention, although the strength coefficient is set to 1.0, may be the strength coefficient appropriately set according to circumstances. In the design method of the present invention, upon although giving derivations elastic Lateral Buckling moment equation (12), in the actual member design, in consideration of the yield and Imperfection steel influence, elastic it is necessary to convert the Lateral buckling moment to design strength. Here, an example equivalent to the steel structure limit state design criteria, the description of the above as AIJ, the conversion calculation of the design strength of an elastic Lateral Buckling moment shown in this document, according to other design criteria and design criteria it may be. Moreover, the bending moment acting on the H-shaped steel beam, the beam (solid line) for receiving the inverse target bending by horizontal load shown in FIG. 13, but to calculate if the vertical load is applied (the dashed line) as a target, FIG. 11A ~ similar effect can be obtained in other load cases shown in FIG. 11D.
[0123]
　Example applying the present invention 1 (H1150 × W300 × tw32 × tf40), Example 2 (H1100 × W280 × tw16 × tf30), ​​Example 3 (H1000 × W250 × tw12 × tf16), Example 4 (H950 × W250 × tw11 × tf25), and the effects of the present invention for each of the example 5 (H850 × W200 × tw10 × tf16) is described by Table 2.
[0124]
　Table 2, all the plastic moment represented by the product of the second moment about the strong axis (Ix), the plastic section modulus around the strong axis (ZXP), design strength of steel (F), ZXP and F the (Mp), shown from the a column to column D, respectively. Incidentally, F is design strength to be determined based on the yield point of the steel in Table 2 (values called steel F value). Incidentally, the yield strength of the steel material may be used as F. In an embodiment, the 325N F / mm 2 ~ 385N / mm 2 although the present invention has to provide a resilient buckling moment, the value of the F value can be used widely.
　Further, the column E ~ G column in Table 2 based on the design method calculation result of the present invention (calculated results based on the present invention), as a result of the H train ~ J column was calculated based on the conventional design method (the prior art the calculation results) based on, the K and L columns show the comparison between the design method and the conventional design method of the present invention. The E column buckling buckling length possible to the Lateral屈補Tsuyoshi without calculated based on the design method of the present invention (Lon), can be a Lateral屈補Tsuyoshi without calculated based on the conventional design method in H column lengths (Loc), it shows a comparison of both the K columns.
From the numerical values shown in column K, it can be seen that possible long enough without the seat屈補rigid and by based on the design method of the present invention to more than four times. Also, if the numerical values shown in column K, to produce a high surface treatment economical shown in tentatively Example In the conventional design method rolled H-section steel, it can not be kept structural economy, ie many Lateral屈補it is not necessary to install a Tsuyoshizai occurs, such surface treatment economically highly rolled H-section steel is shown that has not been utilized conventionally.
　Value indicated by the E column (Lon), in the design method of the present invention, without installing a Lateral屈補Tsuyoshi, a fully plastic moment limit seat屈長of can exhibit (Mp) (Lon). Therefore, the ratio of Mcn to total plastic moment Mp becomes all 1.0 as shown in G column. For the numerical 1.0 is not reduced steel F value, and can use their steel F value as short-term allowable stress against bending Lateral intact. On the other hand, the design strength Mcc shown in column I, based on the conventional design method, set to the same limit locus屈長as the design method of the present invention (Lon), were calculated design strength of the case without the Yokoho Tsuyoshizai it is intended. The ratio to total plastic moment Mp design strength Mcc, as shown in column J, 0.52 at the maximum, minimum is reduced to 0.28. From the fact this number is low, in the conventional design method, it can be understood overlapping that a high rolled H-section steel of the surface treatment economics shown in the Examples are not produced.
　The values shown in L column shows the comparison of the design strength in Lon, the design strength based on the design method of the present invention it can be seen that up to 3.8 times to 1.9 times that of the conventional design method.
[0125]
　Here, the above buckling length Lon is designed proof stress Mcn according to the present invention is a buckling length calculated to be the same value as the fully plastic moment Mp. Further, the above buckling length Loc is designed proof stress Mcc based on conventional design methods are fully plastic moment Mp and buckling length calculated to be the same value.
[0126]
[Table 2]

[0127]
[table 3]

[0128]
　In Table 2, after the example constant, with the design method, it was compared in the present invention and the prior art. In Table 3, the rolled H-shaped steel in the range defined in the prior art in FIG. 6, determined for each example, through performing the specific comparison to those, illustrating the significance of the present invention.
　Against already the embodiments shown, the web thickness tw and the flange thickness tf is constant, the prior art, namely so k is less than 6.1, the height H and width W of the H-shaped steel It was set. That is, the H1050 × W404 × tw32 × tf40 as Comparative Example 1 for Example 1, Example as Comparative Example 2 for 2 H1000 × W369 × tw16 × tf30 , H900 × W352 × tw12 × Comparative Example 3 for Example 3 the TF16, the H900 × W291 × tw11 × tf25 as Comparative example 4 for example 4, are set to Comparative example 5 as H800 × W243 × tw10 × tf16 for example 5.
The A column ~ C column of Table 3, sequentially showing Tsuyojiku around the second moment (Ix), plastic section modulus (ZXP), and steel F value (F). Then, the total plastic moment (Mp) in the D column is calculated as the product of the Zxp and F, the cross-sectional area (S) is in the E column, it shows the outer circumferential length (Lp) to the F column.
To compare the examples and comparative examples, although it is necessary to design strength of flexion Lateral, wherein, based on the design strength (M15) when the buckling length Lb is 15 times the height dimension H Is going. Design strength rolled H-section steel (M15) is the same as the conditions shown in Table 2, each of the calculation results are shown in Column H. Note that the G column shows the percentage of the total plastic yield strength (Mp) of the design strength (M15). As shown in G column, whereas no reduction of the F in the embodiment, it can be seen that the reduced F in a ratio from 0.45 0.76 in the comparative example.
[0129]
　Advantages embodiment for Comparative Examples can be confirmed by the value of N columns from column I. Each column in the case of a 1 to each value of Comparative Example shows the relative values of Examples each value. While a 1.00 Both Ix embodiment, this is because it is dimensioned so that Ix in Comparative Example is consistent with embodiments. From the value of J columns, the relative value of the examples in Zxp embodiment it is found that the decrease in the range of 0.93 0.96. This is because the height dimension of Example (H) is larger than the comparative example.
From the values of K and L columns, the range of the cross-sectional area (S) is 0.90 0.94, and the outer peripheral length (Lp) is seen to decrease in the range of 0.93 to 0.98 .
The value from the design strength (M15) of M columns it is found that the increase in the range of 1.05 2.29. Although the performance is necessary for comprehensive evaluation, and S example of each value indicating the I column to M columns, the molecule Ix and Zxp is desirable value larger, it is the smaller desired value shows the reference value derived in the denominator in the N column Lp.
It can be said that the performance is improved in a range of magnification of the conventional Based on this indicator technology from 1.21 2.50.
[0130]
　Thus, H-shaped steel 1 according to the present embodiment is reduced cross-sectional area S of the beam 2 is at the same time improves the surface treatment economics Ix / Lp, maintain flexural strength higher not only bending rigidity of the beam 2 be able to. Ie, H-shaped steel 1 according to the present embodiment, to improve by both bending stiffness and Lateral column strength of the beam 2, while suppressing local breakdown phenomenon due local buckling of the beam 2, the coating or it is possible to reduce the cost of surface treatment such as painting.
[0131]
　H-beam 1 according to this embodiment, lateral movement despite Lateral屈変shaped beam 2 which is constrained becomes complicated, and the lateral movement of the beam 2 is restrained, the intermediate load from above the upper flange 21 There under conditions acting, elastic Lateral buckling moment M of the beam 2 cr to that calculated from the above (12) to (16), to evaluate the elastic Lateral buckling moment of such steel beam with high precision it is possible.
[0132]
　H-beam 1 according to this embodiment, if in wood axis direction Y of the beam 2 the intermediate load is bent equal to the β (the symmetric buckling) to zero, the intermediate load is equal in wood axis direction Y of the beam 2 bending when not the β on (asymmetric buckling) by a real number ranging from greater than 0 to 3, the case of the equivalent bending moment intermediate load is bent equal and intermediate load antisymmetric moment like that does not equal bending in any case where, in correspondence with the above (12) to (16), taking into account the various load conditions envisaged in real steel beam, evaluate the elastic Lateral buckling moment of steel beam it is possible to become.
[0133]
　H-beam 1 according to this embodiment, in particular, theta y when approximating a is preferably approximated by series of equation (10). H-beam 1 according to this embodiment, when approximating the θy by third term partial sum, dimensionless Lateral Buckling force elastic Lateral Buckling moment divided by the total plastic bending moment (= M cr a / Mp) on the vertical axis, when the slenderness ratio λb obtained by dividing the length l of the beam 2 in RyoNaru a horizontal axis, an example of the analytical solution of the elastic lateral buckling moment is as shown in FIGS. 12A and 12B.
[0134]
　At this time, H-shaped steel 1 according to the present embodiment, as shown in FIG. 12A, when using the series of the (10) equation, the elastic analytical solution of Lateral Buckling moment substantially coincident, the elasticity of the steel beam Lateral the bending moment can be evaluated with a high degree of accuracy. In contrast, as shown in FIG. 12B, when using the Fourier series of the formula (9), becomes the analytical solution of the elastic Lateral Buckling moment varies greatly. At this time, in order to evaluate the elastic Lateral Buckling moment with high accuracy by using a Fourier series of the above (9), for example, theta by paragraph 10 partial sum y since it is necessary to approximate the elastic Lateral Buckling Moment It is the analysis calculation becomes complicated.
[0135]
　Thus, H-shaped steel 1 according to the present invention, theta by series of equation (10) y to approximate the while avoiding the complicated unnecessarily Analysis for Elastic Lateral Buckling Moment , it is possible to evaluate the elastic Lateral buckling moment steel beam with high accuracy.
[0136]
　Incidentally, showing the various rolled H-section steel from Table 4 Table 16. In Tables 4 to 16, "Example" is the above (35) to (38) rolled H-shaped steel which satisfies the equation (invention example), "the prior art" Conventional rolling H-shaped that does not meet these formulas it is steel. Then, for each example and each prior art in Tables 4 to 16, the horizontal axis represents the H / S, shows a graph plotting the vertical axis as Ix / Lp in FIG. In FIG. 14, The symbol "" represents a plot of the Example, "×" represents the plot of the prior art.
[0137]
[Table 4]

[0138]
[table 5]

[0139]
[Table 6]

[0140]
[Table 7]

[0141]
[Table 8]

[0142]
[Table 9]

[0143]
[Table 10]

[0144]
[Table 11]

[0145]
[Table 12]

[0146]
[Table 13]

[0147]
[Table 14]

[0148]
[Table 15]

[0149]
[Table 16]

[0150]
　Having described an embodiment of the present invention, the above embodiments have been presented by way of example, the scope of the present invention is not limited to the embodiments described above. The above embodiments described herein may be embodied in other various forms, without departing from the spirit of the invention, various omissions, substitutions, and changes can be made. The above embodiments and modifications as would fall within the scope and spirit of the invention, and are included in the invention and the scope of their equivalents are claimed.
DESCRIPTION OF SYMBOLS
[0151]
1: rolled H-shaped steel
2: Beam
2a: end
2b: middle part
20: outer peripheral surface
21: upper flange
21a: upper and lower surfaces
21b: left and right end faces
22: lower flange
22a: upper and lower surfaces
22b: left and right end faces
23: Web
23a: left and right side surfaces
23b: curved connecting portion
(fillet) 25: shear connector
3: column
30: diaphragm
4: slab
X: width direction
Y: Material axis direction
Z: height direction

The scope of the claims
[Requested item 1]The upper flange and the lower flange, and has a web connecting the upper flange and the lower flange, a method of designing the top flange, the bottom flange, and a rolled H-shaped steel in which the outer peripheral surface of the web is surface treated a is,
the value obtained by dividing the second moment Ix of about strong axis in circumferential length Lp in the cross-sectional shape when viewed along the timber axis in the cross section perpendicular to the surface treatment economics Ix / Lp, of the cross-sectional shape when the area was S, with satisfying the following (35) to (38) below, the height H from the top flange to the bottom flange is at least 700 mm, each of said upper flange and said lower flange of and the width dimension W is less 1/5 or more and 1/2 of the height dimension H, wherein it is the thickness tw of the web following 32mm or more 9 mm, each of the top flange and the bottom flange As the thickness tf is a 12mm or 40mm or less of the height H, the width W, setting the thickness tw, and the thickness tf
, characterized in that, the design of the rolled H-shaped steel Method.
[Number 28]

[Requested item 2]
　Wherein used as beams rolled H-shaped steel extending in the member axis and condition both ends of the member axis direction of the rolled H-shaped steel is fixed, at an intermediate portion of the member axis, the rolling H-shaped conditions lateral movement in the width direction of the steel is restricted, and the intermediate load is acting vital from above the top flange, under conditions that effect the end load to both ends of the member axis, the following equation (12) elastic Lateral buckling moment M of the beam calculated from ~ (16) cr with, as Lateral buckling in the beam is not generated, the height H, the width W, the thickness tw, and the setting the thickness tf
and wherein the method of designing a rolled H-shaped steel according to claim 1.
　However, V cr : shearing force acting on the end of the timber axis direction of the beam, W cr : intermediate load acting on the intermediate portion of the timber axis direction of the beam, beta and gamma: load V cr , W cr below by (1 ) and (2) coefficient determined from formula, l: beams wood axial length, E: Young's modulus, I: sectional secondary moment about the weak axis of the lower flange, G: shear modulus, J: San · torsional constant of safe, d b : plate thickness center distance between the upper and lower flanges, y: from one end thereof in a timber axis direction of the reference beam to any point of the timber axis direction of the beam length, theta y : Lateral torsion angle caused in the beam by bending, theta ' y : theta yFirst derivative of, theta " y : theta y of the second derivative, a:. A parametric for integrating
Equation 29]

[Expression 30]

[Requested item 3]
　Wherein all plastic moment Mp said elastic Lateral Buckling moment M rolled H-section steel cr as the square root of the value obtained by dividing the is 0.6 or less, the height H, the width W, the thickness tw, and setting the thickness tf
and wherein the method of designing a rolled H-shaped steel according to claim 2.
[Requested item 4]
　The upper flange and lower flange;
　; and the web connecting the upper flange and the lower flange
a rolled H-beam comprising,
　the top flange, the bottom flange, and the outer peripheral surface of the web is treated surfaces;
　said top height H from the flange to the bottom flange is located at least 700 mm;
　the top flange and the width W of each of the lower flange is located 1/5 or more and less than half of the height H;
　the thickness tw of the web be 9mm or 32mm or less;
　; the top flange and the plate thickness tf of each of the lower flange located at 12mm or 40mm or less
　outer periphery in cross section when viewed in the wood axis perpendicular to cross section the value obtained by dividing the second moment Ix of about strong axis length Lp provided as a surface treatment economics Ix / Lp, when the area of the cross section was S, the height dimension H ; The width W, the thickness tw, and the thickness tf is the following (35) to (38) satisfies the formula
rolled H-beams, characterized in that.
[Number 31]

[Requested item 5]The rolling H-shaped of claims 1 to 3 any one rolling H-beams the height H which is set by the design method described, the width W, the thickness tw, and the plate thickness tf producing steel manufacturing method of rolling H-section steel.