Week 2 Challenge
Objective of this challenge is to understand the concept of design of tension members for drilled hole, zigzag bolting and angles section. Also understand the concept of design of sag rods under Dead load and Live load. Know how to determine the section size for given tensile load.
1. Net Area for tension member calculation problem
Problem1.
Here Given parameters are
Size of Plate=(260x20)
Bolt Size = 20mm
Hole dia=20+2=22mm
Net Area for tension is given by
An=(b-nd0+nP^2/4g)t
An=(b-nd0)t Since straight bolt connection nP^2/4g=0
No. of bolts in single straight line in tension failure=4
Therefore, An=(260-4x22)x20=172x20=3440 sqmm.
Problem2
Size of Plate=(260x20)
Bolt Size = 20mm
Hole Dia = 20+2=22mm
An=[(b-nd0)+SumP^2/4g]t
ForAD & BF line of failure, we have
No. of bolts=2
An=[(260-2x22)+0]x20=216x20=4320sqmm
For CEG line of failure
No. of bolts=3
An=[(260-3x22)]x20=260-66x20=214x20=4280sqmm
For ACEG line of failure
No. of bolts=4
An=[(260-4x22)+50x50/4x60]x20=(172+10.42)x20=3648.4sqmm
For ACF
no. of bolts=3
An=[(260-3x22)+50x50/4x60+60x60/4x60]20=(194+10.44+15)20=4388.6sqmm
Thus Min net section area under tension is ACEG.
Hence it is considered as net section area for zig zag bolting.
Problem 3
Angle size=200x100x12
M20 bolts
d0=20+2=22mm
Thus An=(b-nd0+np^2/4g)xt
An=(200-2x22+100x100/4x90)x12
=(156+27.77)x12
=2205.24 sqmm.
2. Sag rod design problem
Given Parameters:
Live Load=75kg/sqmm
self wt. of purlin=100kg/mtr
Wind Pressure = 150kg/sqm
self wt. of roofing = 60kg/sqmtr
Purlin spacing=1.2mtr
Rafter Spacing =8mtr
Total DL= (60+100)x1.2=192kg/m
LL=75x1.2=90kg/m
Wind load=150x1.2=180kg/m
Total Load= DL+LL+WL=192+90+180=462kg/m
We have F=5/8xWxSinθxSx4=5/8x462xSin15x4=2391kgx9.8=23431.8N
F=Rcosθ
R=F/Cosθ=23431.8/Cos15=24258.38N
Area=R/0.6fy
3.14xD^2=Rx4/0.6xfy
or D^2=24258.38x4/0.6x250x3.14(fy=250N/sqmm)
0r D^2=206sqmm
or D=14.3mm
3. Determine section size for given tensile load
Given Parameters
Axial Tensile force=500Kn
Length of angle member=5mtr
fy=350n/sqmm
Net Area An=500x1000/350=1428.57sqmm
From steel table use(100x100x8)mm angle section.
Design Strength of member due to yielding:
Tdg=0.909FyAg=0.909x350x1428.57=454499.5N=454.5KN
Design strength of member tearing of net section for single angles:
Tdn=(0.9AacxFu/Ym1)+(βAg0Fy/Ym0)
Tdn=αxAnfu/Ym1=0.6x1428.57x350/1.1=272727N=272.72KN
Slenderness ratio=Kl/r checked as per IS 800-2007 table8a.