determine ands show on a sketch the principal stresses and t

determine, ands show on a sketch, the principal stresses and the maximum shearing stress at point A in the roof beam in the figure below

8-20. Determine, and show on a sketch, the maxi- stresses and the principal mum shearing stress at point A in the roof beam in Fig. P8-20. 4000 lb Section B-B

Solution

solution:

1)let here given fixed support at 1 and roller support at 2,hence reaction at 1 and 2 are as follows

M1=0

R2y*12-4000*6=0

R2y=2000 lb

Fy=0

R1y=2000 lb

2)here CG or neutral axis passing through 5\'\' from bottom hence tensile bending stresses induced in beam at A

Sb=M*Y/I

where point A is at y=8\'\'

I=I1+I2=b*d^3/12+A*(y1-Y)^2

I=789.33 in4

where bending moment at A around 108\'\' from bottom support 1 from left side of section at A then

M=R1y*(120-12)cos53.13=129600 lb in

hence bending stresses are

Sb=MY/I=129600*(8-5)/789.33=492.56 ib/in2

4)here direct compressive force is also acting at point A,hence compressive stresses are

Sc=F/A

F=4000cos36.87=3199.99 lb

Sc=-3199.99/(32+32)=-49.99 lb/in2

5)here principle stresses at A is given by

Smax=Sb=492.56 lb/in2

Smin=Sc=-49.99 lb/in2

shear stress =tmax=1/2(Sb-Sc)=271.275 lb/in2