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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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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.