Beams 12 and 3 are made of steel Each beam supports a load o

Beams 1,2 and 3 are made of steel. Each beam supports a load of 64 kip, and are supported by beams AC and BD. Dimensions of the beams are as seen on the figure. Normal Stress for the steel is of 24 ksi.

a) Find the cheapest (least cross-sectional area) S-shape steel beam for the beams 1, 2, and 3.

b) Repeat (a) but with a W-shape steel beam

PD: Appendixes of properties of rolled steel S (American Standard Shapes) and W (Wide Flange Shapes) shapes were given for this problem.

Solution

solution:

1)here beam 1,2,3 are supported by two beam AC and BD ,which takes load on it equally

2)load on beam 1,2,3 assumed to be distrubuted uniformly,hence analysis of beam AC is similar to meam BD and meam 1 is similar to 2,3.

3)here for beam AC

support reaction are Ra and RC and it takes half load 32 kips from each beam

Ma=0

Ra=Rc=32(4+12+20)/24=48 kips

hence bending mement is

Ma=Mc=0

M1=48*4=192 kips

M2=48*12-32*8=320 kips

M3=192 kips

hence bendimg stress would be

Sb=M2*y/I

Z=I/y

as 1 ft=12\'\'

Z=M2/Sb=320*12/24=159.96

for this section modulus perfect beam from table is

s beam is S20*96

W beam is W12*120

4)where for beam 1,assuming load distrubuted uniformly between support support reactio are

R1=R1\'=64/2=32 kips

where maximum moment would occure midway between supports

M=32*(12/2)=192 kips

hence bending stress and section modulus is given by

Z=I/y=M/Sb=192*12/24=96 in^3

for this section modulus perfect beam are

s beam is S18*70

w beam is W12*72