A steel beam with overhanging ends and wide flange cross sec

A steel beam with overhanging ends and wide flange cross section is supported as shown below. The beam carries a uniform load of q = 8 k/ft on each overhang. Assuming that the section modulus of the cross sectional area is S = 414 in^3, determine the maximum bending stress in the beam (ksi) due to load q.

Solution

Given data :

UDL = 8 K/ft

Section modulus = 414 in^3

Assume points

Point at Free end denoted with A

Point at left support denoted with B

Point at right support denoted with C

Point at right side free end denoted with D

Taking moment about B

Apply law equilibrium

Clockwise moment = anti clockwise moments

8*10*(10/2 +20)=Rc *20 + 8*10*10/2

20Rc =1600

Rc = 80 K

Rb + Rc = 8*10 +8*10=160k

Rb = 160-80=80k

Shear force :-

At A = 0

At just before B = 8*10=80k

At B = 80-Rb = 80-80= 0

At C = 0-Rc = -80k

At D = -80+8*10=0

Bending moment :-

At A =0

At B = -8*10*10/2=-400kft

At C = -8*10(10/2 +20)+80*20= -400kft

At D = -8*10(10/2 +30)+80*30+80*10-8*10*10/2

=0

Maximum bending moment offers at shear force equal to zero. Shear force is zero in between the portion of BC. Bending moment at this portion is 400 kft which is maximum.

Maximum bending moment

Mmax = 400 kft = 4800 kIn

Bending equation

f = Mmax/Z

f = 4800/414=11.59 ksi

Maximum bending stress (f)=11.59 ksi