An R.C.C beam of 25 cm width has a clear span of 5 metres and carries a U.D.L. of 2000 kg/m inclusive of its self weight. If the lever arm of the section is 45 cm., the beam is
A. Safe in shear
B. Is safe with stirrups
C. Is safe with stirrups and inclined members
D. Needs revision of the section
Answer: Option A
Step-1 Max Shear force Simply Supported Beam =Vmax= wL/2 = (2000x5)/2 = 5000 kg
Step-2 Nominal Shear Force Produced due to External Loading for Simply Supported Beam =Vmax / bd =5000/25x45 = 4.44 kg./cm2.
Step-3 Check for Permissible Shear Stress in Section
Condition i. if < 5 kg/cm2 i.e Safe in Shear no reinforcement required.
Condition ii. if b/w 5kg/cm2 i.e to 20 kg/ cm2 Safe in shear but shear Reinforcement Needed.
Condition iii. if > 20 kg/cm2 i.e Section needed to redesign.
As Nominal Shear is 4.44 kg/cm2 which is < 5 kg/cm2 so Beam is Safe in Shear with no reinforcement needed.
As,
Max value of shear stress without striups is 5kg/cm^2
Calculate the stress due to load=shearforce/area
=(2000*5/2)/45*25=4.44
Which is less than 5
Hence it is safe in shear
Lever arm = d-(n/3) #depth of NA = d/2
Substituting value of lever arm and n ...d=54cm
Assuming overall depth with Clear cover ( +25)
D= 80 cm approx or 0.8m ...
S.F= WL/2 : S.F= 5000kg/m2 = 50KN/m2
Shear Stress = S.F/bd = 250KN/m2 =0.25N/mm2
Hence Safe ( as Shear stress < 0.5 N/mm2)
tariq meo
SF = 2000 ÷ (500 * 100) = 0.04 kg/sq cm.
Safe shearing stress = L/A
Load = 20 * 500 = 10000 kg.
Area = 25 * 45 = 1125 sq cm.
Therefore L/A = 8.88 kg/sqcm.
Hence Safe shearing stress > shear force.
Result : Beam is safe in shear.
How to it calculate