Homework 4 

Example 1: A rectangular beam 60 mm wide and 150 mm deep is simply supported over a span of 6 m. If the beam is subjected to central load of 12 kN, find the maximum bending stress induced in the beam section. 



Given: b = 60 mm h = 150 mm L = 6 m = 6 000 mm W = F = 12 kN = 12 000 N Req: σ_{b max }= ? Solution: σ_{b max }= (M_{max }y_{max})/(I_{min}) ………..(1)
M_{max }= FL/4 = (12 000 x 6 000) / 4 = 18 000 000 Nm
Y_{max} = h/2 = 150/2 = 75 mm
I_{min}= I= bh^{3}/12 = (60 x 150^{3}) /12 = 16875000 mm^{4}
From eqn. (1)
σ_{b max }= 80 MPa (Ans.)

σ_{b max }= 80 MPa 
1 A cantilever beam is rectangular in section having 80 mm width and 120 mm depth. If the cantilever is subjected to a point load of 6 kN at the free end and the bending stress is not to exceed 40 MPa, find the span of the cantilever beam (1.28 m) 



2 A Hollow square section with outer and inner dimensions of 50 mm and 40 mm respectively is used as a cantilever of span 1 m. How much concentrated load can be applied at the free end of the cantilever, if the maximum bending stress is not to exceed 35 MPa? (430.5 N) 



3 A hollow steel tube having external and internal diameter of 100 mm and 75 mm respectively is simply supported over a span of 5 m. The tube carries a concentrated load of F at distance of 2 m from one of the supports. What is the value of F, if the maximum bending stress is not to exceed 100 MPa. (5.6 kN) 


