Week 2 Challenge
1.Ans.:
Plate - Drilled Hole:
Solution:
We know,Net section area = (b-nd)t
Given,b=260mm , t=20mm , d=20mm but d0=20+2=22mm and n=4
Therefore, An=(260-4(22))20 =3440mm2
Plate - Zigzag bolting:
Solution:
We know, Net section area = (b-nd+sum(P2/4g))t
Given, b=260mm , t=20mm , d=20mm but d0= 20+2=22mm
case 1 :
Along section AD or BF :
An=(260-2(22))20=4320mm2
case 2 :
Along section CEG :
An= (260-3(22))20 = 3880mm2
case 3 :
Along section ACEG :
An = (260-4(22)+60^2/4(60))20 = 3740mm2
case 4 :
Along section BCEG :
An = (260-4(22)+50^2/4(60))20=3648.33mm2
case 5 :
Along section ACF :
An= (260-3(22)+60^2/4(60)+50^2/4(60))20 = 3948mm2
The minimum value is the net section area , Hence An= 3648.33mm2
Angle (200 x 100 x 12 with M20 bolt):
Solution:
We know , Net section area = (b-nd+sum(P2/4g))t
Given , angle section: 200mm x 100mm , t=12mm,d= 200mm but d0 = 20+2=22mm
An = (200+100-3(22)+50^2/4(90)+50^2/4(130))12 = 2949.02mm2
2.Ans.:
Assume centre to centre distance of Rafter spaced at 8m , spacing of purlin = 1.2m , self weight of roofing (including thermal insulation)=60kg/m2 , wind pressure intensity = 150kg/m2 , slope of rafter =15degrees , Live Load = 75kg/m2
Assume self weight of purlin as 100kg/m
Solution:
DL+LL=(60+75)*9.8*1.2*8 = 12700
Load on each sag road = (12700/3+100*9.8*8/3)Sin(15) = 6846.66*Sin (15) = 1772N
Therefore , we know
Load on threaded rod , Tdn = 0.9*An*fu/1.25
1772 = 0.9*An*fu/1.25
An = 1772*1.25/(0.9*250) (fu = 250Mpa)
An = 9.844
d = (4*An/pi)^0.5
d = 3.54mm
3.Ans.:
Assume 4mm weld size , fy=250MPa , fu= 410MPa
Approximate gross area = 1.1Tdg/fy=1.1x250x1000/250=1100mmA2
from steel table , select ISA 100x75x8mm
connected to gusset plate by longer length Cxx
area of connected leg = (100-8/2)x8=768mm2
area of outstanding length = (75-8/2)x8=568mm2
Ag=768+568=1336mm2>1100mm2 , hence Safe.
Design strength due to yielding of gross section ,
Tdg=Agfy/rmo = 1336x250/1100 = 303.94kN
Design strength due to rupture at net section ,
Tdn=alpha*An*fu/rml
fu = 0.8x1336x410/1000
fu=438.21kN
Design strength due to block shear ,
for calculation of block shear , length of weld is required
P1x100=250x(100-31) = 172.50kN
P2=250-172.50 = 77.5kN
Strength of 4mm weld = 0.7x4x0.462x410 =530.37kn/mm
Effective length of weld on head side = 172.5x1000/530.37 = 325mm
Effective length of weld on toe side = 77.5x1000/530.37 = 146mm
Total welded length = 325+146 = 471mm
Avg = Avn = 471x8 = 3768mm2
Atg= Atn = 100x8 = 800mm2
Tdb1 = 0.525Avg x fy +0.72xAtnxfy = 0.525x3768x250/1000+0.72x800x410/1000 = 730.31kN
Tdb2 = 0.416Avnxfu+0.91xAtgxfy = 0.416x3768x410/1000+0.91x800x250/1000 = 824.67kN
Tensile strength provided = 438.21 kN , 303.94kN and 730.71 kN >250kN
Hence safe.