Week 2 Challenge
SOLUTION 1
A....
CHAIN BOLTING=
PLATE SIZE =260*20 MM
FOR A 20 MM BOLT
BOLT DIAMETER= 22 MM
NET AREA =(B-N*D@0)*T
NET AREA =(260-4*22)*20=3440 MM^2
SOLUTION 1
B.....
ZIG ZAG BOLTING
PLATE SIZE =260*20 MM
FOR A 20 MM BOLT
BOLT DIAMETER= 22 MM
PATH AD= TWO HOLES
PATH BF= TWO HOLES
PATH CEG = THREE HOLES
PATH ACEG =FOUR HOLES AND ONE STAGGER
PATH BCEG =FOUR HOLES AND ONE STAGGER
PATH ACF =THREE HOLES AND TWO STAGGER
PATH BCD =THREE HOLES AND TWO STAGGER
PATH ACD = THREE HOLES AND TWO STAGGER
PATH BCF= THREE HOLES AND TWO STAGGER
PATH AD AND BF=TWO HOLES
A@N=(B-N*D@0)T=(260-2*22)20=4320 MM^2
PATH CEG = THREE HOLES
A@N=(B-N*D@0)T=(260-3*22)20=3880 MM^2
PATH ACEG =FOUR HOLES AND ONE STAGGER
A@N=[(B-N*D@0+SIGMA(P^2/4*G)]T=[(260-4*22)+60^2/4*60]20=3740 MM^2
PATH BCEG =FOUR HOLES AND ONE STAGGER
A@N=[(B-N*D@0+SIGMA(P^2/4*G)]T=[(260-4*22)+50^2/4*60]20=3648.33 MM^2
PATH ACF OR BCD =THREE HOLES AND TWO STAGGER
A@N=[(B-N*D@0+SIGMA(P^2/4*G)]T=[(260-3*22)+60^2/4*60+50^2/4*60]20=4388 MM^2
PATH ACD = THREE HOLES AND TWO STAGGER
A@N=[(B-N*D@0+SIGMA(P^2/4*G)]T=[(260-3*22)+60^2/4*60+60^2/4*60]20=4480 MM^2
PATH BCF= THREE HOLES AND TWO STAGGER
A@N=[(B-N*D@0+SIGMA(P^2/4*G)]T=[(260-3*22)+50^2/4*60+50^2/4*60]20=4296.67 MM^2
THE MINIMUM NET AREA IS FOR PATH BCEG =3648 MM^2.
SOLUTION 1
C.....
DATA GIVEN
ANGLE SECTION(200*100*12)
BOLT SIZE =20 MM
GAUGE**=g1+g2-t
GAUGE**=70+60-12
GAUGE**=118 MM
A@N=A@G-SIGMA(D@H*T)+SIGMA[(P^2/4*G)]T
A@G=288*6=1728 MM^2
PATH AC=
NET AREA=(1728-2*22)12
NET AREA =1464 MM^2
PAT ABC
NET AREA =1728-3*22*12+[(50^2/4*90+50^2/4*118)]12
NET AREA =1082.8932 MM^2
THE MINIMUM NET AREA IS FOR PATH ABC=1082.89 MM^2.
SOLUTION 2
SAG ROD PROBLEM
SELF WEIGHT OF ROOF=60KG/M^2=588.399 N/M^2
DEAD LOAD ON ROOF=588.399*1.2=706.0788 N/M
SELF WEIGHT OF PURLIN =100 KG/M=980.665 N/M
LIVE LOAD =75 KG/M^2=735.49875 N/M^2
LIVE LOAD ON PURLIN =735.49875*1.2=882.5985 N/M
TOTAL GRAVITY LOAD =706.0788+980.665+882.5985=2569.3423 N/M
WIND LOAD =150 KG/M^2=1470.9975 N/M^2
WIND LOAD (NORMAL TO ROOF)=1470.9975*1.2=1765.197 N/M
COMPONENT OF GRAVITY LOAD (PARALLEL TO ROOF)=2569.3423*SIN15=664.9947 N/M
PULL ON SAG ROD=664.9947*8/3=1773.3192 N
FACTORED LOAD=1773.3192*1.5=2659.9788 N
REQUIRED NET AREA=T@DN*GAMMA@M1/(0.9*F@U)
NET AREA=2659.9788*1.25/0.9*410=9.01 MM^2
PROVIDE A 16 MM DIAMETER SAG ROD BETWEEN PURLINS
NOTE =THE PROVIDED ROD SHOULD NOT BE LESS THAN 16 MM IN DIAMETER
SOLUTION 3
GIVEN DATA
T=500 KN
FACTORED T=500*1.5=750 KN
FY= 350 N/MM^2
FU=490 N/MM^2
L = 3000 MM
ASSUMING.
FOR A 20 MM BOLT
BOLT DIAMETER= 22 MM
PITCH =40 MM
GAUGE= 40 MM
EDGE DISTANCE =40 MM
A@G(REQ)=TDG*GAMMA@M0/FY=750*10^3*1.1/350=2357.14 MM^2
INCREASING AREA BY 40 PERCENT WE GET
A@G(REQ)=3300 MM^2=33 CM^2
LAMDA=KL/R
KL=3000 MM
R=350 FROM TABLE (FROM TABLE 3 OF IS800-2007)
LAMDA=KL/R
350=3000/R
R=8.571 MM =0.85 CM
SELECTING ANGLE 200*200*12 MM (INCREASING SINCE FAILING IN RUPTURE)
AREA PROVIDED =46.61 CM^2=4661 MM^2
R MIN PROVIDED=3.92 CM=39.2 MM
AREA PROVIDED> A@G(REQ)
4661 MM^2>3300 MM^2
ASSUME 20 MM DIA BOLT OF 12 NUMBER THAT IS 4 BOLT IN 3 ROWS EACH
DESIGN STRENGTH DUE TO YIELDING
TDG=FY*AG/GAMMA@MO=350*4661/1.1=1483045.455 N OR 1483.045 KN
TDG>T
1483.045 KN>750 KN HENCE SAFE.
DESIGN STRENGTH DUE TO RUPTURE
TDN=ALPHA*AN*FU/GAMMA M1
ALPHA=0.8
AN=A1+KA2
A1=(200-12/2-3*22)12=1536 MM^2
A2=(200-12/2)*12=2328 MM^2
K=3A1/3A1+A2=3*1536/3*1536+2328=0.6643
AN=1536+0.6643*2328=3082.62 MM^2
TDN=0.8*3082.62*490/1.25=966712.692 N OR 966.712692 KN
TDN= 966.712692 KN>750 KN HENCE SAFE
DESIGN STRENGTH DUE BLOCK SHEAR
ATG=(40+60+60)12=1920 MM^2
ATN=(40+60+60-2.5*22)=1260 MM^2
AVG=(40+60+60+60)12 =2640 MM^2
AVN=(40+60+60+60-3.5*22)12=1716 MM^2
TDB1=AVG*FY/SQUAREROOT*3*GAMMA@MO+0.9*ATN*FU/GAMMA@M1
TDB1=2640*350/SQUAREROOT*3*1.1+0.9*2160*490/1.25
TDB1=929502.2261 N
TDB1=929.5022 KN >750 KN HENCE SAFE
TDB2=0.9*AVN*FU/SQUAREROOT*3*GAMMA@M1+ATG*FY/GAMMA@M0
TDB2=0.9*1716*490/SQUAREROOT*3*1.25+*1920*350/1.1
TDB2=960439.715 N
TDB2=960.4397 KN >HENCE SAFE
TENSION CAPACITY OF ANGLE=929.50 KN > 750 KN HENCE SAFE
CHECK FOR STIFFNESS
TABLE 3 OF CODE
KL/R
3000/39.2=76.53 <350 HENCE SAFE