An R.C.C. beam of 6 m span is 30 cm wide and has a lever arm of 55 cm. If it carries a U.D.L. of 12 t per m and allowable shear stress is 5 kg/cm2, the beam
A. Is safe in shear
B. Is safe with stirrups
C. Is safe with stirrups and inclined bars
D. Needs revision of section
Answer: Option D
we know that moment M=V*LA where LA is liver arm (for given signs F=verticle shear force, v=horizontal shear force, x=longitudinal distance)
now v=M/LA , also M=F*x
shear stress S=V/(B*x)
S=F/(B*LA)
for question:
S=12000*6/2*(30*55)=21.82 >8 kg/cm^2 hence unsafe
Divide 12000 kg with 55*30 we will get 7.27 kg/sqcm but in question allowable shear stress is 5kg/sqcm so it will fail and section needs to be redesign.
can any one explain this question