is800 2007 single angle detailed calculation
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DESCRIPTION
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Page 1 of 4
This detailed calculation corresponds to IS800_2007_Single
Angle.pdf
Problem Description
Solution: Member Length L = 2.83 m
Material: Fe250 FYLD = 250 MPa, FU = 420 MPa, E = 2.05E+05 MPa
Section: ISA 80X50X8
Check against Slenderness Ratio (As per Table 3, Section 3.8)
Effective Length factor along Local Y-Axis = KY = 0.8
Effective Length factor along Local Z-Axis = KZ = 0.9
Slenderness ratio about Z axis = z = 240.28
Slenderness ratio about Y axis = y = 84.07
Maximum Slenderness Ratio = 240.28
The section is safe against slenderness check as the allowable ratio in Axial
Tension is 400.
Section Classification (As per Table 2, Section 3.7.2 and 3.7.4)
= SQRT (250/FYLD) = 1
For Axial Compression:
b/t = 6.25 < 15.7=15.7
Thus, Class is Semi-Compact for Short Leg.
The marked member of the structure is to
be designed against IS-800:2007 (LSM)
and the results are computed
subsequently. The member is laterally
unsupported.
The design values are as follows:
Design Forces 47 KN (Tension)
0.048 KNm (Bending-Z)
0.0844 KN (Shear-Y)
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Page 2 of 4
d/t = 10 < 15.7=15.7
The class is Semi-Compact for Long Leg.
(b+d)/t = 16.25 < 25 = 25
Thus, Overall Class is Semi-Compact.
Thus, Effective Area for Axial Compression = (d + b t)*t = 978 mm2
For Bending:
b/t = 6.25 < 9.4=9.4
Thus, Class is Plastic for Short Leg.
d/t = 10 < 10.5=10.5
The class is Compact for Long Leg.
Thus, Overall Class is Compact.
Calculation of tension capacity (As per Section 6.2 and 6.3)
Net Section Factor = NSF = 1
Design against block shear is not performed. Thus, DBS = 0.0
Partial safety factor for failure in tension by yielding = m0 = 1.1 (As per Table 5)
Partial safety factor against ultimate tension failure by rupture = m1 = 1.25(As per Table 5)
Factor for calculation of tearing strength of net section depends on no of bolts,
ALPHA = 0.7 (As per Section 6.3.4)
Net area of cross section = Anet = 978 mm2
Strength as governed by yielding of gross section = Tdg = 222.27 kN
Strength as governed by tearing of net section = Tdn = 230.03 kN
Design tensile strength of the the member (minimum of Tdg and Tdn) = 222.27 kN
Ratio = 0.212 < 1.0
Design of member subjected to Compression (As per Section 7.1)
Partial factor of safety of material = mo = 1.1
Buckling class of cross-section
(As per Table10, Section 7.1.2.2 & Table7, Section 7.1.2.1)
Buckling class along Y-Y = c
Buckling class along Z-Z = c
Imperfection factor about Y axis = y = 0.49
Imperfection factor about Z axis = z = 0.49
Design calculations (As per Section 7.1.2.1)
Euler buckling stress about Z axis = fcc-z = 35.072 MPa
Non-dimensional effective slenderness ratio about Z axis = z = 2.67
z = 4.67
Design compressive strength of the member about Z axis = fcd-z = 26.738 MPa
Euler buckling stress about Y axis = fcc-y = 286.51 MPa
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Non-dimensional effective slenderness ratio about Y axis = y = 0.934
y= 1.116
Design compressive strength of the member about Y axis = fcd-y = 131.6 MPa
Design Compressive Stress = fcd = 26.738 MPa < fy / mo
Factored load (Capacity) = Pd = 26.15 kN (As per Section 7.1.2)
Design of member subjected to Shear Capacity along Y-Axis: Shear area = Avy = D*t = 640 mm
2
Design shear strength (As per Sec. 8.4 and 8.4.1) = Fvdy = 84 kN
Ratio = 1.01E-03 < 1.0
Capacity along Z-Axis: Shear area = Avz = B*t = 400 mm
2
Design shear strength (As per Sec. 8.4 and 8.4.1) = Fvdz = 52.5 kN
Design of member subjected to Bending
Steel section properties
Plastic Section modulus of the section (Along Z-Axis) = Zpz = 8670 mm3
Plastic Section modulus of the section (Along Y-Axis) = Zpy = 23000 mm3
Elastic Section modulus of the section (Along Z-Axis) = Zez = 4570 mm3
Elastic Section modulus of the section (Along Y-Axis) = Zey = 13265 mm3
Moment carrying capacity along Z-Axis
The member is not laterally supported. Thus, LAT = 0.0
For Major-Axis (As per Section 8.2.2)
Check for Lateral Torsional Buckling
Modulus of Rigidity = G = 78846.1 mm3
Torsional Constant = It = 2.09E+04 mm4
Warping Constant = Iw = 7627548 mm6
Effective Length for lateral torsional buckling = LX = KX*L = 0.85*2830 = 2406 mm
Elastic lateral buckling moment (As per Section 8.2.2.1) = Mcr = 20222231.77 N.mm
b = 1 (As per Section 8.2.2)
lt = 0.21 (As per Section 8.2.2)
Non-dimensional slenderness ratio = lt = 0.327 > SQRT (1.2*Zez*FYLD/Mcr) = 0.26
Hence, lt =0.26
lt = 0.54
lt = 0.987 < 1.0
Design moment for Lateral Torsional Buckling = Mdz = 1.94 kN.m
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Ratio = 0.0246 < 1.0
For Minor-Axis: (As per Section 8.2.1.2)
Critical Ratio for Shear = 0.00 < 0.6
The deflection pattern is of simply supported type and Bending Class is Compact.
Thus, CAN = 0.0, and b = 1.0
Mdy1 = 5.23E+06 Nmm > 1.2*Zey*FYLD/mo = 3.59E+06 N.mm
Design bending strength = Mdy = 3.59 kN.m
Interaction Check:
Check for Section Strength to the combined effects of loading (As per Section 9.3.1)
Axial strength = Nd = 222273 N
Mdy = 3.59E+06 N.mm
Mdz = 1.94E+06 N.mm
Since the section is a Angle-section, Clause 9.3.1.1
Interaction Ratio = 0.236 < 1.0
The section is safe against the Combined Axial Tension and Bending
Check for Overall Member Strength to the combined effects of loading
Check for Bending and axial tension (As per Section 9.3.2.1)
PSI = 1.0
MeffY = negative
Interaction Ratio for Y-Axis = 0.0 < 1.0
The section is safe
MeffZ = negative
Interaction Ratio for Z-Axis = 0.0 < 1.0
The section is safe
Thus, the critical ratio is 0.236.
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