FLEXURAL & SHEAR STRENGTH OF DOUBLY SYMMETRIC I-SHAPED MEMBERS
BASED ON AISC 360-2010 DESIGN CODE
Material Strength
fy =
Es =
Steel Grade =
Yield Strength =
Elastic Modulus =
SS400 (16 mm < t ≤ 40 mm)
235.00
MPa
200,000.00
MPa
Ws =
A=
Ix =
Iy =
rx =
ry =
Sx =
Sy =
Zx =
Zy =
J=
Cw =
Dimension Properties
Beam Member =
Self Weight =
Cross Section Area =
Moment of inertia about the x-axis =
Moment of inertia about the y-axis =
Radius of gyration about the x-axis =
Radius of gyration about the y-axis =
Elastic section modulus about the x-axis =
Elastic section modulus about the y-axis =
Plastic section modulus about the x-axis
Plastic section modulus about the y-axis
Torsional Constant =
Warping Constant =
IWF 450 x 200 x 9 x 14
76.00
Kg/m
9,398.00
mm^2
322,589,452.67
mm^4
18,692,303.17
mm^4
185.27
mm
44.60
mm
1,433,730.90
mm^3
186,923.03
mm^3
1,621,489.00
mm^3
297,091.00
mm^3
471,814.67
mm^4
888,333,015,692.67
mm^6
Design Shear Strength
Strong Axis Design Shear Strength
h/tw ≤ 2.46 x (Es/Fy)
Bassically Not Required Transverse Stiffeners
Use Stiffener =
No
1.00
x H.iwf
a=
Stiffener Spacing =
450.00
mm
φv =
Resistance Factor =
0.90
Cv.y =
Web Shear Coefficient =
1.00
Vn.y =
Nominal Shear Strength about y-axis =
571.05
kN
φVn.y =
Design Shear Strength about y-axis =
513.95
kN
Weak Axis Design Shear Strength
Cv.x =
Web Shear Coefficient =
1.00
Vn.x =
Nominal Shear Strength about x-axis =
789.60
kN
φVn.x =
Design Shear Strength about x-axis =
710.64
kN
Custom Steel Grade
Fy =
Yield Strength =
600.00
MPa
300
200
100
0
-300
-200
-100
0
100
-100
Custom Profile Dimension
-200
Design Method
Design Method =
Steel Shape Making Process =
I Shaped
h/tw Condition =
LRFD
Built Up
-300
Web & Flange Classification
Web Classification =
Flange Classification =
L=
Compact Web
Compact Flange
Design Flexural Strength
Applied AISC Moment Provision =
Beam Length =
Lb Fraction =
Lb =
Lp =
Lr =
Lb Condition =
Cb =
Mnx =
Mny =
φ=
φMn.x =
φMn.y =
Nominal Flexural Strength about x-axis =
Nominal Flexural Strength about y-axis =
Resistance Factor =
Design Flexural Strength about x-axis =
Design Flexural Strength about y-axis =
Ratio (Mnx/Mpx) =
Ratio (Mny/Mpy) =
IWF 400 x 200 x 3 x 13 (Custom)
F2
2.00
1/1
2.00
2,289.85
6,796.23
Lb ≤ Lp
1.00
381.05
69.82
0.90
342.94
62.83
100%
100%
m
xL
m
mm
mm
H=
B=
tw = t1 =
tf = t2 =
r=
Height of Beam =
Width of Beam =
Web Thickness =
Flange Thickness =
Armpit radius =
Dimension Properties
Self Weight =
49.63
Moment of inertia about the x-axis =
2.0785E+08
Web & Flange Classification
Web Classification =
Not Compact Web
Flange Classification =
Compact Flange
AISC 360-10 Proportioning Limit for I-Shaped Members Check
h/tw =
124.67
h/tw max =
260.00
Aw/Af.c =
0.43
Aw/Af.c max =
10.00
Ws =
Ix =
kN.m
kN.m
kN.m
kN.m
400.00
200.00
3.00
13.00
3.00
Definition =
Cb = Lateral-torsional buckling modification factor for nonuniform moment diagrams
Lb = Length between points that are either braced against lateral displacement of the compression flange or braced against twist of the cross section
Lp = The limiting laterally unbraced length for the limit state of yielding
Lr = The limiting unbraced length for the limit state of inelastic lateral-torsional buckling
XX
=> Editable Value
mm
mm
mm
mm
mm
Kg/m
mm4
OK!
OK!
Created by:
Civil Studio
Email: civilpande.studio@gmail.com
Version 1.0 (2020)
200
300
FLANGES AND WEB LOCAL STRENGTH DUE TO CONCENTRATED FORCES
BASED ON AISC 360-2010 DESIGN CODE
Material Strength
fy =
Es =
Steel Grade =
Yield Strength =
Elastic Modulus =
H.iwf =
B.iwf =
tw =
tf =
r=
k=
Dimension Properties
Beam Member =
Total Height of Beam =
Width of Beam =
Web Thickness =
Flange Thickness =
Armpit radius =
tf + r =
300
SS400 (16 mm < t ≤ 40 mm)
235.00
MPa
200,000.00
MPa
200
100
IWF 450 x 200 x 9 x 14
450.00
mm
200.00
mm
9.00
mm
14.00
mm
18.00
mm
32.00
mm
0
-300
-200
-100
0
100
200
300
-100
-200
Design Method
Design Method =
Steel Shape Making Process =
LRFD
Built Up
-300
I. Flange Local Bending Strength
This section applies to tensile single-concentrated forces and the tensile component of doubleconcentrated forces
Concentrated Force Position from the Member End =
Bigger than 10 x tf
10 x tf =
140.00
mm
0.15 x bf =
30.00
mm
φ=
Reduction Factor =
0.90
Rn =
6.25 x fy x tf =
20.56
kN
φRn =
φ x Rn =
18.51
kN
Note =
If the length of loading across the member flange is less than 0.15 x bf, Flange local bending need not be
checked.
=> When required, a pair of transverse stiffeners shall be provided
IV. Web Local Yielding Strength
This section applies to single-concentrated forces and both components of doubleconcentrated forces
φ=
lb =
Reduction Factor =
1.00
Length of bearing =
200.00
mm
Case Applied =
Case 1
Case 1 = The concentrated force to be resisted is applied at a distance from the member end that is
greater than the depth of the member
Rn =
fy x tw x (5 x k + lb) =
761.40
kN
φRn =
φ x Rn =
761.40
kN
Note =
lb not less than k for end beam reactions
k = Distance from outer face of the flange to the web toe of the fillet
=> When required, a pair of transverse stiffeners or a doubler plate shall be provided
II. Web Local Crippling Strength
This section applies to compressive single-concentrated forces or the compressive component of doubleconcentrated forces
φ=
Reduction Factor =
0.75
lb =
Length of bearing =
200.00
mm
d=
Full nominal depth of the section =
450.00
mm
lb/d =
0.44
> 0.2
Case Applied =
Case 1
Case 1 = The concentrated compressive force to be resisted is applied at a distance from the member
end that is greater than or equal to d/2
Rn =
934.86
kN
0.8 x tw^2 x (1 + 3 x lb/d x (tw/tf)^1.5) x √((E x fy x
tf)/tw) =
φRn =
φ x Rn =
701.14
kN
Note =
lb not less than k for end beam reactions
k = Distance from outer face of the flange to the web toe of the fillet
=> When required, a transverse stiffener, a pair of transverse stiffeners, or a doubler plate extending at
least one-half the depth of the web shall be provided.
III. Web Compression Buckling Strength
This section applies to a pair of compressive single-concentrated forces or the compressive components
in a pair of double-concentrated forces, applied at both flanges of a member at the same location.
φ=
Reduction Factor = =
0.90
Force Location from End =
Bigger than d/2
h=
H.iwf - (2 x tf) =
422.00
mm
Rn =
(24 x tw^3 x √(E x Fy)) / h =
284.23
kN
φRn =
φRn =
255.81
kN
=> When required, a single transverse stiffener, a pair of transverse stiffeners, or a doubler plate
extending the full depth of the web shall be provided.
V. Web Sideways Buckling Check
This section applies only to compressive single-concentrated forces applied to members where
relative lateral movement between the loaded compression flange and the tension flange is not
restrained at the point of application of the concentrated force
φ=
Reduction Factor =
0.85
h=
H.iwf - (2 x tf) =
422.00
mm
bf =
Width of flange =
200.00
mm
Cr =
Coefficient for web sidesway buckling =
3,310,000.00
MPa
L=
Beam Length =
2,000.00
mm
Lb Fraction =
1/1
xL
Lb =
2,000.00
mm
(h/tw) / (Lb/bf) =
4.69
Compression Flange Condition Against Rotation =
Not Restrained
(h/tw) / (Lb/bf) > 1.7, web sidesway buckling does not apply
Rn =
Cr x tw^3 x tf/ h^2 x (0.4 x (h/tw) / (Lb/B.iwf)^3) =
7,822.19
kN
φRn =
φ x Rn =
6,648.86
kN
Note =
Lb = Largest laterally unbraced length along either flange at the point of load
h = clear distance between flanges less the fillet or corner radius for rolled shapes; distance between
adjacent lines of fasteners or the clear distance between flanges when welds are used for built-up
shapes
Cr = 960,000 ksi (6.62x10^6 MPa) when Mu < My (LRFD) or 1.5Ma < My (ASD) at the location of the
force
Cr = 480,000 ksi (3.31x10^6 MPa) when Mu ≥ My (LRFD) or 1.5Ma ≥ My (ASD) at the location of the
force
=> When the required strength of the web exceeds the available strength, local lateral bracing shall be
provided at both flanges at the point of application of the concentrated forces
XX
=> Editable Value
STIFFENER DESIGN
Transverse Stiffener Design for Beam
Minimum Transverse Stiffener Moment of Inerta Requirement
IWF 450 x 200 x 9 x 14
Bassically Not Required Transverse Stiffeners
450.00
mm
Stiffener Spacing =
422.00
mm
Effective Height of Web =
450.00
mm
Total height of beam =
200.00
mm
Width of beam =
9.00
mm
Web Thickness =
14.00
mm
Flange Thickness =
0.50
Stiffener bending rigidity parameter =
164,025.00
mm^4
a x tw^3 x j =
Minimum Transverse Stiffener Thickness Requirement
Stiffener =
Single
Offset from edge of flange =
10.00
mm
Width of stiffener =
85.50
mm
Height of stifffener =
368.00
mm
Minimum stiffener thickness =
7.00
mm
Beam Member =
a=
h=
H.iwf =
B.iwf =
tw =
tf =
j=
I.req =
ofs =
b=
h=
t.min =
Bearing Stiffener Design for Beam
1. Bearing Strength of Bearing Stiffener
Design Method =
LRFD
fy =
Yield Strength =
235.00
E=
Elastic Modulus =
200,000.00
φ=
Resistance Factor =
0.75
ofs =
Offset from edge of flange =
10.00
cl =
Cope hole dimension =
20.00
b.br =
Width of stiffener =
85.50
t.min = Stiffener minimum thickness =
6.11
t.use =
Used bearing stiffener thickness =
12.00
Check t.use =
OK!
Apb =
2 x (b.br - cl) x t.use =
1,572.00
Rn =
1.8 x Apb x fy =
664.96
φRn =
φ x Rn =
498.72
2. Bearing Stiffener as Column Strength
Bearing Stiffener Location =
Interior
k.L =
316.50
Effective column height =
bw =
225.00
Effective web width =
Radius Gyration of Bearing Stiffener
Ib =
5,844,939.75
Moment of Inertia =
Ag =
4,077.00
Cross Section Area =
r=
37.8634
√(Ib/Ag) =
Design Compressive Strength
φ=
0.90
Resistance Factor =
λ=
8.36
k.L/r =
Fe =
8,992.32
Elastic buckling stress =
Fcr =
232.44
Critical Stress =
Pn =
947.67
Fcr x Ag =
φPn =
852.91
φ x Pn =
XX
=> Editable Value
MPa
MPa
mm
mm
mm
mm
mm
mm^2
kN
kN
mm
mm
mm^4
mm^2
mm
MPa
MPa
kN
kN
ANALYSIS OF SIMPLE BEAM
STEEL PROPERTIES
Steel Profil =
L=
Beam Span =
Lb =
Laterally Unbraced Length =
Ix =
Moment of Inertia =
q.SW =
Self Weight of Steel Beam =
Es =
Steel Elastic Modulus =
Design Method =
IWF 450 x 200 x 9 x 14
2.00
m
2.00
m
322,589,452.67
mm^4
0.76
kN/m
200,000.00
MPa
LRFD
LOAD MULTIPLIER FACTOR
δ1 =
δ2 =
For Dead Load =
For Live Load =
XX
1.20
1.60
=> Editable Value
BEAM WITH DISTRIBUTED LOAD
BEAM WITH POINT LOAD
q.DL =
q.LL =
UNIFORMLY DISTRIBUTED LOAD
Distributed Dead Load =
Distributed Live Load =
0.00
0.00
kN/m
kN/m
P.DL =
P.LL =
CONCENTRATED LOAD AT CENTER
Point Dead Load =
Point Live Load =
qa =
qu =
TOTAL DISTRIBUTED LOAD
q.SW + q.DL + q.LL =
δ1 x [q.SW + q.DL] + δ2 x q.LL =
0.76
0.91
kN/m
kN/m
Moment Strength Ratio
1/8 x qu x L^2 =
Design Flexural Strength about x-axis =
Check =
Mu / ØMn.x =
qa =
qu =
Pa =
Pu =
q.SW =
δ1 x [q.SW] =
P.DL + P.LL =
δ1 x P.DL + δ2 x P.LL =
0.46
342.94
OK!
0.001
kN.m
kN.m
Shear Strength Ratio
qu x L/2 =
Design Shear Strength about y-axis =
Check =
Vu / ØVn.y =
0.91
513.95
OK!
0.002
kN
kN
Mu =
φMn.x =
SR =
Vu =
φVn.y =
SR =
Δ.max =
Δ.all =
Ratio =
Δ.max =
Δ.all =
Ratio =
Vu =
Maximum Deflection
Due to DL
5 x (q.SW + q.DL) x L^4 / (384 x E x Ix) =
L/360 =
Check =
Δ.max / Δ.all =
Due to DL + LL
5 x qa x L^4 / (384 x E x Ix) =
L/240 =
Check =
Δ.max / Δ.all =
kN
kN
0.76
0.91
0.00
0.00
kN/m
kN/m
kN
kN
Moment Strength Ratio
1/8 x qu x L^2 =
Pu x L/4 =
Mu.1 + Mu.2 =
Design Flexural Strength about x-axis =
Check =
Mu / ØMn.x =
0.46
0.00
0.46
342.94
OK!
0.001
kN.m
kN.m
kN.m
kN.m
0.91
0.00
0.91
513.95
OK!
0.002
kN
kN
kN
kN
SR =
Shear Strength Ratio
qu x L/2 =
Pu/2 =
Vu.1 + Vu.2 =
Design Shear Strength about y-axis =
Check =
Vu / ØVn.y =
Ru =
Vu =
0.91
kN
TOTAL LOAD
Mu.1 =
Mu.2 =
Mu =
φMn.x =
Support Reaction
Ru =
0.00
0.00
0.91
kN
0.00
5.56
OK!
0.000
mm
mm
0.00
8.33
OK!
0.000
mm
mm
SR =
Vu.1 =
Vu.2 =
Vu =
φVn.y =
Support Reaction
Δ.max.1 =
Δ.max.2 =
Δ.max =
Δ.all =
Ratio =
Δ.max.1 =
Δ.max.2 =
Δ.max =
Δ.all =
Ratio =
Maximum Deflection
Due to DL
5 x (q.SW) x L^4 / (384 x E x Ix) =
P.DL x L^3 / (48 x E x Ix) =
Δ.max.1 + Δ.max.2 =
L/360 =
Check =
Δ.max / Δ.all =
Due to DL + LL
5 x qa x L^4 / (384 x E x Ix) =
Pa x L^3 / (48 x E x Ix) =
Δ.max.1 + Δ.max.2 =
L/240 =
Check =
Δ.max / Δ.all =
`
0.00
0.00
0.00
5.56
OK!
0.000
mm
mm
mm
mm
0.00
0.00
0.00
8.33
OK!
0.000
mm
mm
mm