STRUCTURAL STEEL DESIGN OF W, HP, M, S
Beam dimensions and mechanical properties of materials
Yield strength:
F y = 3515 kg/cm²
Ultimate strength:
F u = 4570 kg/cm²
Young's modulus:
E = 2039000 kg/cm²
Poisson's ratio:
v = 0.300
Shear modulus of elasticity:
G = 784231 kg/cm²
Flexural buckling factors and Stiffeners parameters
30.2
L b = 300.00 cm
18.9
PNA
396.0
W14X159 (HR - 356 mm x 236.7 kg/m)
General geometric properties
Lateral Torsional Buckling modification:
C b = 1.000
Gross area:
A g = 301.29 cm²
Flexural buckling about z-axis:
K z = 1.000
Net area:
A n = 299.78 cm²
Flexural buckling about y -axis:
K y = 1.000
Perimeter:
P = 4068.623 cm
Torsional buckling about longitudinal axis: K x = 1.000
Unit weight of the element:
W = 236.62 kg/m
Consider stiffeners?
Net depth:
h = 32.030 cm
Distance between flange centroids:
h 0 = 35.100 cm
Consider Tension Field Action?
Twice distance from ENA to face of CF:
h c = 32.030 cm
Second order effects are considered in the
determination of the normal stresses?
Twice distance from PNA to face of CF:
h p = 32.860 cm
Product of inertia:
I zy = 0 cm⁴
a = 500.00 cm
Clear distance between stiffeners:
J = 820.0 cm⁴
Saint Venant torsion constant:
Forces
Warping constant:
C w = 9559877 cm⁶
Axial force in compression:
P Uc = 22.851 t
Horizontal distance edge-shear center:
e 0 = 0.000 cm
Shear force about minor axis
V Uz = 13.200 t
Shear center z -coordinate:
z 0 = 0.000 cm
Shear force about major axis
V Uy = 8.800 t
Shear center y -coordinate:
y 0 = 0.000 cm
Bending about major axis
M Uz = 35.200 t-m
Polar moment of inertia:
I 0 = 110218 cm⁴
Bending about minor axis
M Uy = 52.800 t-m
Polar radius of gyration (shear center):
r 0 = 19.126 cm
Torsion:
T U = 2.200 t-m
Geometric properties of compression flange
Geometric properties of tension flange
Compression flange gross area:
A fc = 119.59 cm²
Tension flange gross area:
A ft = 119.59 cm²
Compression flange moment of inertia:
I yc = 15628 cm⁴
Tension flange moment of inertia:
I yt = 15628 cm⁴
Distance compression flange - web:
k c = 4.55 cm
Distance compression flange - web:
k t = 4.55 cm
Radius or fillet considered:
k des-c - t c = 1.52 cm
320.6
Laterally unbraced length:
ENA
z
30.2
t t = 3.020 cm
164.3
Tension flange thickness:
160.2
t c = 3.020 cm
15.2
Compression flange thickness:
15.2
b t = 39.60 cm
190.5
Tension flange width:
198.0
y
190.5
b c = 39.60 cm
351.0
Compression flange width:
198.0
45.5
t w = 1.890 cm
320.3
Web thickness:
396.0
45.5
d = 38.10 cm
381.0
Overall depth:
Radius or fillet considered:
k des-t - t t = 1.52 cm
Geometric properties bent about their major axis:
Geometric properties bent about their minor axis:
Distance between centroid to end CF:
y (+) = 19.05 cm
Distance between centroid to end CF:
z (+) = 19.80 cm
Distance between centroid to end CT:
y (-) = 19.05 cm
Distance between centroid to end CT:
z (-) = 19.80 cm
Moment of inertia:
I z = 79084 cm⁴
Moment of inertia:
I y = 31134 cm⁴
Radius of gyration:
r z = 16.21 cm
Radius of gyration:
r y = 10.16 cm
Plastic section modulus:
Z z = 4703 cm³
Plastic section modulus:
Z y = 2393 cm³
Elastic section modulus - compression:
S zc = 4162 cm³
Elastic section modulus - compression:
S yc = 1576 cm³
Elastic section modulus - tension:
S zt = 4162 cm³
Elastic section modulus - tension:
S yt = 1576 cm³
Shape factor:
αz = 1.130
Shape factor:
αy = 1.518
Shear area major axis:
A w = 72.01 cm²
Shear area minor axis:
A f = 239.18 cm²
Flexural buckling about major axis: K z L b /r z = 18.513
Flexural buckling about minor axis: K y L b /r y = 29.528
Compression flange yield moment:
M ycz = 146.305 t
Compression flange yield moment:
M ycy = 55.412 t
Tension flange yield moment:
M ytz = 146.305 t
Tension flange yield moment:
M yty = 55.412 t
Plastic moment:
M pz = 165.314 t
Plastic moment:
M py = 84.097 t
Summary
Chapter D
Chapter E
0.00%
2.56%
Chapter F
Chapter G
major axis
minor axis
major axis
minor axis
23.71%
69.76%
5.79%
2.91%
Chapter H
96.78%
|
Elastic (Euler) buckling forces and stresses
Elastic stress for buckling bent about the major axis:
𝐹𝑒𝑧 =
Elastic stress for buckling abent about the minor axis:
𝐹𝑒𝑦 =
𝜋 2𝐸
𝐾𝑧 𝐿𝑏 2
𝑟𝑧
𝜋 2𝐸
𝐾𝑦 𝐿𝑏 2
𝑟𝑦
Elastic stress for buckling bent about the longitudinal axis: 𝐹𝑒𝑥 =
= 58720 kg/cm²
==>
𝑃𝑒𝑧 = 𝐹𝑒𝑧 𝐴 = 17691.619 t
= 23081 kg/cm²
==>
𝑃𝑒𝑦 = 𝐹𝑒𝑦 𝐴 = 6954.184 t
1 𝜋 2 𝐸𝐶𝑤
+ 𝐺𝐽 =25229 kg/cm²
𝐴𝑟02 𝐾𝑦2 𝐿2𝑏
Width-thickness ratios for compression elements
Coefficient for unstiffened slender elements: 𝜆𝑤 =
ℎ
= 15.3 ==> 0.35
𝑡𝑤
< 𝑘𝑐 =
4
ℎ
𝑡𝑤
= 1.023
>
0.76
==>
𝑘𝑐 = 0.760
Width-thickness ratio of compression flange: 𝜆𝑐 = 6.540
<
λ𝑟𝑐 = 0.64
𝑘𝑐 𝐸
= 13.438 ==> Compression flange not slender
𝐹𝑦
Width-thickness ratio of web:
𝜆𝑤 = 15.300
<
λ𝑟𝑤 = 1.49
𝐸
= 35.887 ==> Web not slender
𝐹𝑦
Width-thickness ratio of tension flange:
𝜆𝑡 = 6.540
<
λ𝑟𝑡 = 0.64
𝑘𝑐 𝐸
= 13.438 ==> Tension flange not slender
𝐹𝑦
Width-thickness ratios for flexural elements
λ𝑝𝑐 = 0.38
Width-thickness ratio of
compression flange:
λ c = 6.540
𝐸
= 9.152
𝐹𝑦
==> Compact Compression Flange
𝑘𝑐 𝐸
λ𝑟𝑐 = 0.95
= 19.947
𝐹𝐿
ℎ𝑐 𝐸
ℎ𝑝 𝐹𝑦
λ𝑝𝑤 =
Width-thickness ratio of web: λ w = 15.300
Width-thickness ratio of
tension flange:
2
𝑀𝑝𝑧
0.54
− 0.09
𝑀𝑦𝑧
=86.769
==> Compact Web
λ𝑟𝑤 = 5.70
𝐸
= 137.284
𝐹𝑦
λ𝑝𝑡 = 0.38
𝐸
= 9.152
𝐹𝑦
λ t = 6.540
==> Compact Tension Flange
𝑘𝑐 𝐸
λ𝑟𝑡 = 0.95
= 19.947
𝐹𝐿
Chapter D. Design of members for tension
𝑃𝑛 = 𝐹𝑦 𝐴𝑔 = 1059.03 t
D.a) Strength for tensile yielding:
D.b) Minimum strength for tensile rupture in connected members:
If only the compression flange is connected:𝑈𝑓𝑐 =
𝐴𝑓𝑐
= 0.397
𝐴𝑔
𝐴𝑒𝑐 = 𝑈𝑓𝑐 𝐴𝑛 = 118.99 cm²
==>
𝑃𝑛𝑐 = 𝐹𝑢 𝐴𝑒 =
If only the web is connected:
𝑈𝑤 =
𝐴𝑤
= 0.239
𝐴𝑔
𝐴𝑒𝑤 = 𝑈𝑓𝑐 𝐴𝑛 = 71.65 cm²
==>
𝑃𝑛𝑤 = 𝐹𝑢 𝐴𝑒 = 327.43 t
If only the tension flange is connected:
𝑈𝑓𝑐 =
𝐴𝑓𝑡
= 0.397
𝐴𝑔
𝐴𝑒𝑡 = 𝑈𝑓𝑐 𝐴𝑛 = 118.99 cm²
==>
𝑃𝑛𝑡 = 𝐹𝑢 𝐴𝑒 = 543.79 t
0.000 t
==>
The nominal stress is:
𝑃𝑛 = 327.429 t
Resistance factor is:
ϕ𝑡 = 0.9
𝛟𝒕 𝑷𝒏 = 294.686 t
The reduced tension strength of the element is:
>
Chapter E. Design of members for compression
E.a) Constants for torsional or flexural-torsional elastic buckling stress:
𝜎𝑒𝑦
𝑎1 =
𝑦 2
𝑥0 2
+ 𝜎𝑒𝑥 0 − 𝜎𝑒𝑥 − 𝜎𝑒𝑦 − 𝜎𝑒𝑧
𝑟0
𝑟0
=-107030
𝑥 2 + 𝑦2
1− 0 2 0
𝑟0
𝑎2 =
𝜎𝑒𝑦 𝜎𝑒𝑧 + 𝜎𝑒𝑥 𝜎𝑒𝑦 + 𝜎𝑒𝑥 𝜎𝑒𝑧
1−
𝑥02 + 𝑦02
𝑟02
𝑎3 = −
𝜎𝑒𝑦 𝜎𝑒𝑦 𝜎𝑒𝑧
1−
𝑥02 + 𝑦02
𝑟02
𝑎5 =
3𝑎2 − 𝑎12
= -133130040
9
9𝑎1 𝑎2 − 27𝑎3 − 2𝑎13
=1.516E+12
54
=3419058131
θ = acos −
= -3.419E+13
𝜃 𝑎1
𝐹𝑒1 = −2 −𝑎4 cos − =23081 kg/cm²
3 3
Torsional or flexuraltorsional elastic
buckling stress:
𝑎4 =
𝜃 + 2𝜋
𝑎1
𝑎5
−𝑎4 3
= 2.9803
543.79 t
0.00%
Torsional or flexuraltorsional elastic
buckling stress:
𝐹𝑒2 = −2 −𝑎4 cos
𝜃 + 2𝜋 𝑎1
− =58720 kg/cm²
3
3
𝐹𝑒3 = −2 −𝑎4 cos
𝜃 + 4𝜋 𝑎1
− =25229 kg/cm²
3
3
==> will be taken:
F e = 23081 kg/cm²
E.b) The nominal stress:
𝐹𝑦
𝐹𝑛 = 0.658𝐹𝑒 𝐹𝑦 = 3297.9 kg/cm²
𝐹𝑛 = 0.877𝐹𝑦 = 3082.7 kg/cm²
==>
==>
𝐾𝑧 𝐿𝑏
= 18.51
𝑟𝑧
<
𝐾𝑦 𝐿𝑏
= 29.53
𝑟𝑦
<
𝐾𝑥 𝐿𝑏
= 15.69
𝑟0
<
The nominal stress is:
𝐹𝑛 = 3297.9 kg/cm²
Resistance factor is:
ϕ𝑐 = 0.9
The nominal compressive strength is:
==> 3297.9 kg/cm²
𝐸
=
𝐹𝑦 113.44
4.71
==> 3297.9 kg/cm²
==> 3297.9 kg/cm²
𝑃𝑛 = 𝐹𝑛 𝐴 = 993.637 t
𝛟𝒄 𝑷𝒏 = 894.273 t
The reduced compressive strength of the element is:
22.851 t
>
==>
Chapter F. Design of members for flexure bent about their major axis
ℎ𝑐 𝑡𝑤
= 0.506
Ratio of 2 times the area of ​the web in compression to the area of ​the compressed flange: 𝑎𝑤 =
𝑏𝑐 𝑡𝑐
𝑏𝑐
Effective radius of gyration for lateral-torsional buckling:
𝑟𝑡 =
=10.978 cm
1
12 1 + 𝑎𝑤
6
4
Coefficient for unstiffened slender elements:
0.35 < 𝑘𝑐 =
>
0.76 ==> 𝑘𝑐 = 0.760
= 0.972
ℎ
𝑡𝑤
Nominal compression flange stress above which inelastic buckling limit states apply:
𝑆𝑧𝑡
=
𝑆𝑧𝑐 1.00 >
0.70
==>
𝐹𝐿 = 𝐹𝑦
𝑆𝑧𝑡
=
𝑆𝑧𝑐 3515 kg/cm²
>
==>
F L = 2461 kg/cm²
𝜆𝑤 − 𝜆𝑝𝑤
=1.314
𝜆𝑟𝑤 − 𝜆𝑝𝑤
==> 𝑅𝑝𝑐 = 1.130
0.5𝐹𝑦 = 1758 kg/cm²
F.a.1) Flexural strength for members with compact or non-compact webs
F.a.1.1 Compression Flange Yielding (CFY)
𝐼𝑦𝑐
= 0.502
𝐼𝑦
ℎ𝑐
= 15.30
𝑡𝑤
<
𝑅𝑝𝑐 =
0.23
==>
<
𝜆𝑝𝑤 = 86.769
𝑅𝑝𝑐 =
𝑀𝑝𝑧
𝑀𝑝𝑧
−
−1
𝑀𝑦𝑐𝑧
𝑀𝑦𝑐𝑧
The Nominal Flexural Strength Compression Flange Yielding is:
F.a.1.2 Lateral-Torsional Buckling (LTB)
Unbraced limit length for elastic lateral-torsional buckling:
𝑀𝑝𝑧
= 1.130
𝑀𝑦𝑐𝑧
𝑅𝑝𝑐 = 1.000
𝑀𝑛 = 𝑅𝑝𝑐 𝑀𝑦𝑐𝑧 = 165.314 t-m
(Check for lateral torsional buckling)
𝐿𝑝 = 1.1𝑟𝑡
𝐸
= 290.841 cm
𝐹𝑦
2.56%
Unbraced limit length for inelastic lateral-torsional buckling: 𝐿𝑟 = 1.95𝑟𝑡
If L p < L b ≤ L r :
If L b > L r :
𝐿𝑏 − 𝐿𝑝
𝐿𝑟 − 𝐿𝑝
𝑀𝑛 = 𝐶𝑏 𝑅𝑝𝑐 𝑀𝑦𝑐𝑧 − 𝑅𝑝𝑐 𝑀𝑦𝑐𝑧 − 𝐹𝐿 𝑆𝑧𝑐
𝑀𝑛 =
𝐶𝑏 𝜋 2 𝐸𝑆𝑧𝑐
𝐿𝑏 2
𝑟𝑡
𝐽
𝐿𝑏
1 + 0.078
𝑆𝑧𝑐 ℎ0 𝑟𝑡
𝐸
𝐽
+
𝐹𝐿 𝑆𝑧𝑐 ℎ0
𝐽
𝑆𝑧𝑐 ℎ0
2
+ 6.76
164.966 t-m
=
==> 𝑀𝑛 = 164.966 t-m
2
= 1292.015 t-m
𝐹𝐿 2
1946.719 cm
=
𝐸
165.314 t-m
>
F.a.1.3 Compression Flange Local Buckling (FLB)
Sections with non-compact flange:
𝑀𝑛 = 𝑅𝑝𝑐 𝑀𝑦𝑐𝑧 − 𝑅𝑝𝑐 𝑀𝑦𝑐𝑧 − 𝐹𝐿 𝑆𝑧𝑐
𝜆𝑐 − 𝜆𝑝𝑐
=180.535 t-m
𝜆𝑟𝑐 − 𝜆𝑝𝑐
==> 𝑀𝑛 = 165.314 t-m
0.9𝐸𝑘𝑐 𝑆𝑧𝑐
𝑀𝑛 =
= 1357.228 t-m
𝜆2𝑐
Sections with slender flange:
F.a.1.4 Tension Flange Yielding (TFY)
𝐼𝑦𝑐
= 0.502
𝐼𝑦
ℎ𝑐
= 16.95
𝑡𝑤
<
𝑅𝑝𝑡 =
0.23
==>
<
𝑅𝑝𝑡 =
𝜆𝑝𝑤 = 86.769
𝑀𝑝𝑧
𝑀𝑝𝑧
−
−1
𝑀𝑦𝑡𝑧
𝑀𝑦𝑡
𝑀𝑝𝑧
= 1.130
𝑀𝑦𝑡𝑧
==> 𝑅𝑝𝑡 = 1.130
𝜆𝑤 − 𝜆𝑝𝑤
=1.314
𝜆𝑟𝑤 − 𝜆𝑝𝑤
𝑅𝑝𝑡 = 1.000
𝑀𝑛 = 𝑅𝑝𝑡 𝑀𝑦𝑡𝑧 = 165.314 t-m
The Nominal Flexural strength by Tension Flange Yielding is:
F.a.2) Bending strenght for membes with slenderness web
F.a.2.1 Compression Flange Yielding (CFY)
Bending strength reduction factor:
𝑅𝑝𝑔 = 1 −
𝑎𝑤
ℎ𝑐
𝐸
− 5.7
1200 + 300𝑎𝑤 𝑡𝑤
𝐹𝑦
=1.045
>
1.00 ==> 𝑅𝑝𝑔 = 1.000
𝑀𝑛 = 𝑅𝑝𝑔 𝑀𝑦𝑐𝑧 =146.305 t-m
The Nominal Flexural Strenght by Compression Flange Yielding is:
F.a.2.2 Lateral-Torsional Buckling (LTB)
(Check for lateral torsional buckling)
Unbraced limiting length for elastic lateral torsional buckling:
𝐿𝑝 = 1.1𝑟𝑡
Unbraced limiting length for inelastic lateral-torsional buckling:
𝐿𝑟 = 𝜋𝑟𝑡
𝐸
= 992.804 cm
0.7𝐹𝑦
If L p < L b ≤ L r :
𝐿𝑏 − 𝐿𝑝
𝐿𝑟 − 𝐿𝑝
=145.733 t-m
If L b > L r :
𝑀𝑛 = 𝑅𝑝𝑔 𝑆𝑧𝑐 𝐶𝑏 𝐹𝑦 − 0.3𝐹𝑦
𝑀𝑛 =
𝑅𝑝𝑔 𝑆𝑧𝑐 𝐶𝑏 𝜋 2 𝐸
𝐿𝑏 2
𝑟𝑡
=1121.612 t-m
𝐸
= 290.841 cm
𝐹𝑦
==> 𝑀𝑛 = 145.733 t-m
>
146.305 t-m
𝜆𝑐 − 𝜆𝑝𝑐
𝜆𝑟𝑐 − 𝜆𝑝𝑐
=156.927 t-m
F.a.2.3 Compression Flange Local Buckling (FLB)
Sections with non-compact flange:
Sections with slender flange:
𝑀𝑛 = 𝑅𝑝𝑔 𝑆𝑧𝑐 𝐹𝑦 − 0.3𝐹𝑦
𝑀𝑛 =
0.9𝐸𝑘𝑐 𝑅𝑝𝑔 𝑆𝑧𝑐
𝜆2𝑐
==> 𝑀𝑛 = 146.305 t-m
= 1357.228 t-m
F.a.2.4 Tension Flange Yielding (TFY)
𝑀𝑛 = 𝑀𝑦𝑡𝑧 = 146.305 t-m
The Nominal Flexural Strenght by Tension Flange Yielding is:
Resistance factor is:
ϕ𝑏 = 0.9
The nominal bending strength of the element is: 𝑀𝑛 = 164.966 t-m
𝛟𝒃 𝑴𝒏𝒛 = 148.469 t-m
The reduced bending strength of the element is:
>
35.200 t-m
==>
23.71%
Chapter F. Design of members for flexure bent about their minor axis
F.b.1 Compression Flange Yielding:
𝑀𝑛 = 𝑀𝑝𝑦 = 84.097 t-m
<
1.6𝐹𝑦 𝑆𝑦𝑐 = 88.659 t-m
𝑀𝑛 = 84.097 t-m
==>
F.b.2 Compression Flange Local Buckling (FLB)
For sections with non-compact flange: 𝑀𝑛 = 𝑀𝑝𝑦 − 𝑀𝑝𝑦 − 0.7𝐹𝑦 𝑆𝑦𝑐
For sections with slender flange:
𝑀𝑛 =
𝑀𝑛 = 𝑀𝑝𝑦 =84.097 t-m
F.b.3 Tension Flange Yielding:
𝜆𝑐 − 𝜆𝑝𝑐
=95.061 t-m
𝜆𝑟𝑐 − 𝜆𝑝𝑐
0.7𝐸𝑆𝑦𝑐
𝜆2𝑐
= 526.061 t-m
1.6𝐹𝑦 𝑆𝑦𝑡 = 88.659 t-m
<
==> 𝑀𝑛 = 84.097 t-m
==> 𝑀𝑛 = 84.097 t-m
F.b.4 Tension Flange Local Buckling (FLB)
For sections with non-compact flange: 𝑀𝑛 = 𝑀𝑝𝑦 − 𝑀𝑝𝑦 − 0.7𝐹𝑦 𝑆𝑦𝑐
For sections with slender flange:
𝜆𝑡 − 𝜆𝑝𝑡
=95.061 t-m
𝜆𝑟𝑡 − 𝜆𝑝𝑡
𝑀𝑛 =
Resistance factor is:
ϕ𝑏 = 0.9
The nominal shear strength is:
𝑀𝑛 = 84.097 t
0.7𝐸𝑆𝑦𝑐
𝜆2𝑡
𝑀𝑛 = 84.097 t-m
= 526.061 t-m
𝛟𝒃 𝑴𝒏𝒚 = 75.687 t-m
The reduced bending strength of the element is:
==>
>
52.800 t-m
==>
69.76%
Chapter G. Design of members subjected to Major-Axis Shear
If
Shear buckling
coefficient:
𝑎
= 15.610
ℎ
>
5
𝑘𝑣 = 5 +
= 5.021
𝑎 2
ℎ
3.0
if the stiffeners are not
considered:
k v = 5.340
It is taken: ==> k v = 5.340
G.a.1 Shear strenght without considering the diagonal tension field:
𝜆𝑤 =
ℎ
= 15.30
𝑡𝑤
𝐸
= 53.95
𝐹𝑦
<
2.24
<
𝑘𝑣 𝐸
1.1
= 61.22
𝐹𝑦
C v1 = 1.000
==>
1.10
𝐶𝑣1 =
𝑘𝑣 𝐸
𝐹𝑦
ℎΤ𝑡𝑤
==> 𝐶𝑣1 = 1.000
=4.001
𝑉𝑛 = 0.6𝐹𝑦 𝐴𝑤 𝐶𝑣1 =151.867 t
The nominal shear strength without considering the diagonal tension field is:
𝜆𝑤 =
ℎ
= 15.30
𝑡𝑤
<
𝐸
= 61.18
𝐹𝑦
2.54
Transverse stiffeners are not required
G.a.2 Shear strength in interior web panels considering the diagonal tension field:
𝐶𝑣2 = 1.000
1.1
𝑘𝑣 𝐸
= 61.22
𝐹𝑦
>
𝜆𝑤 =
ℎ
= 15.30
𝑡𝑤
> 1.37
𝑘𝑣 𝐸
= 0.874
𝐹𝑦
𝐶𝑣2 =
ℎΤ𝑡𝑤
𝐶𝑣2 =
1.1
𝑘𝑣 𝐸
= 61.22
𝐹𝑦
>
2𝐴𝑤
= 0.602
𝐴𝑓𝑐 + 𝐴𝑓𝑡
<
ℎ
= 0.809
𝑏𝑓𝑐
<
𝜆𝑤 =
ℎ
= 15.30
𝑡𝑤
==>
2.500
==>
𝑉𝑛 = 0.6𝐹𝑦 𝐴𝑤 𝐶𝑣2 +
<
ℎ 2
𝐹𝑦
𝑡𝑤
==> 𝐶𝑣2 = 1.000
= 19.981
1 − 𝐶𝑣2
𝑎 2
1.15 1 +
ℎ
1 − 𝐶𝑣2
𝑎
𝑎 2
+ 1+
ℎ
ℎ
1.15
ℎ
= 0.809
𝑏𝑓𝑡
1.51𝑘𝑣 𝐸
= 4.001
𝑉𝑛 = 0.6𝐹𝑦 𝐴𝑤 = 151.867 t
𝑉𝑛 = 0.6𝐹𝑦 𝐴𝑤 𝐶𝑣2 +
6.00
𝑘𝑣 𝐸
𝐹𝑦
1.10
6.00
The nominal shear strength in interior web panels considering the diagonal tension field is:
=151.867 t
=151.867 t
𝑉𝑛 = 151.867 t
Shear strength:
Resistance factor is:
ϕ𝑉 = 1.0
The nominal shear strength is:
𝑉𝑛 = 151.867 t
𝛟𝑽 𝑽𝒏𝒚 = 151.867 t
The reduced shear strength of the element is:
<
8.800 t
==>
5.79%
Chapter G. Design of members subjected to Minor-Axis Shear
G.b.1 Compression flange shear strength:
k v = 1.200
C v2 = 1.000
1.1
𝑘𝑣 𝐸
= 29.02
𝐹𝑦
>
𝜆𝑐 =
𝑏𝑐
=
2𝑡𝑐
6.540 <
1.37
𝑘𝑣 𝐸
= 36.15
𝐹𝑦
1.10
𝐶𝑣2 =
𝐶𝑣2 =
Shear strength in compression flange:
𝑉𝑛𝑐 = 0.6𝐹𝑦 𝑏𝑐 𝑡𝑐 𝐶𝑣2 = 252.220 t
𝑘𝑣 𝐸
𝐹𝑦
𝑏𝑐
2𝑡𝑐
1.51𝑘𝑣 𝐸
𝑏𝑐 2
𝐹𝑦
2𝑡𝑐
= 4.438
= 24.575
==> 𝐶𝑣2 = 1.000
G.b.2 Tension flange shear strength:
C v2 = 1.000
1.1
𝑘𝑣 𝐸
= 29.02
𝐹𝑦
>
𝜆𝑐 =
𝑏𝑡
=
2𝑡𝑡
6.540 <
1.37
𝑘𝑣 𝐸
= 29.02
𝐹𝑦
1.10
𝐶𝑣2 =
𝐶𝑣2 =
Shear strength in tension flange:
𝑘𝑣 𝐸
𝐹𝑦
𝑏𝑐
2𝑡𝑐
1.51𝑘𝑣 𝐸
𝑏𝑡 2
𝐹𝑦
2𝑡𝑡
=4.438
==> 𝐶𝑣2 = 1.000
= 24.575
𝑉𝑛𝑡 = 0.6𝐹𝑦 𝑏𝑡 𝑡𝑡 𝐶𝑣2 =252.220 t
Resistance factor is:
ϕ𝑉 = 0.9
The nominal shear strength is:
𝑉𝑛 = 504.439 t
𝛟𝑽 𝑽𝒏𝒛 = 453.995 t
The reduced shear strength of the element is:
<
13.200 t
==> 2.91%
Chapter H. Design of members for combined forces and torsion
When second order effects, if any, are considered in the determination of the normal stresses:
𝑓𝑟𝑎 =
𝐹𝑐𝑎 =
𝑃𝑈
= 75.8 kg/cm²
𝐴
ϕ𝑐 𝑃𝑛
= 2968.2 kg/cm²
𝐴
𝑓𝑟𝑏𝑧 =
𝐹𝑐𝑏𝑧 =
𝑀𝑈𝑧
= 845.7 kg/cm²
𝑆𝑧
ϕ𝑏 𝑀𝑛𝑧
= 3567.0 kg/cm²
𝑆𝑧
𝑓𝑟𝑏𝑦 =
𝐹𝑐𝑏𝑦 =
𝑀𝑈𝑦
= 3349.3 kg/cm²
𝑆𝑦
ϕ𝑏 𝑀𝑛𝑦
= 4801.2 kg/cm²
𝑆𝑦
𝑓𝑟𝑎
𝑓𝑟𝑏𝑥 𝑓𝑟𝑏𝑦
+
+
= 0.9602
𝑓𝑟𝑏𝑥 𝐹𝑐𝑏𝑥 𝐹𝑐𝑏𝑦
q.2 If second order effects occur but are not considered in determining the normal stresses, the following equation must be
used:
𝑓𝑟𝑏𝑦
𝑓𝑟𝑎
𝑓𝑟𝑏𝑧
+
+
=0.9678
𝑃𝑢
𝑃
0.8𝐹𝑐𝑎
1−
𝐹
1 − 𝑢 𝐹𝑐𝑏𝑦
𝑃𝑒𝑧 𝑐𝑏𝑧
𝑃𝑒𝑦
The combined stresses of the element is:
==> 96.78%
Nodo
BUILTUP
BEAMS
ROLLE
D
BEAMS
Perfil:
Coordenadas
x (mm) y (mm)
1
19.80
-38.10
PL 198,-381 198,-350.8 9.45,-350.8 9.45,-30.2 198,-30.2 198,0 -198,0 -198,-30.2
2
19.80
-35.08
3
0.95
-35.08
1
Sí
1
4
0.95
-3.02
2
No
1
5
19.80
-3.02
6
19.80
0.00
7
-19.80
0.00
8
-19.80
-3.02
9
-0.95
-3.02
10
-0.95
-35.08
11
-19.80 -35.08
12
-19.80 -38.10
13
19.80
2
-38.10
201
b) Concentrated force strengths / Flexural buckling factors.
Concentrated axial force (H-section):R U = 0.000 t
Length of bearing:
l b = 5.00 cm
Distance concentrated force-member end: d b = 5.00 cm
9.45,-350.8 9.45,-30.2 198,-30.2 198,0 -198,0 -198,-30.2 -9.45,-30.2 -9.45,-350.8 -198,-350.8 -198,-381 198,-381