Computation of Shear Stress of Beam

Problem 1. Determine the shear stress of a rectangular beam having shear of V and cross sectional dimension is b x h ?
Exam Name: Easteni Refinery Ltd. 2017

Solution:
We know,
Shear stress,     τ = VQ / Ib
               Here,V = V
                        Q = AӮ
                            = b * h/2 * h/4
                            = bh²/8
                          I = bh³ / 12
                          b = b

                     ∴  τ = VQ / Ib
                            =  (V* bh²*12)/ 8 *  b² * h³
                            = 3V/ 2bh
     
 Answer: 3V/ 2bh

---

Problem 2. Calculate maximum shear stress of a rectangular beam having dimension of (6" x 12") and vertical shear 48 kips?
Exam Name: BPDB 2016, PGCB 2015


Solution:
We know,
Shear stress,     τ = VQ / Ib
               Here,V =48 kips
                        Q = AӮ
                            =  6 * (12/2) * (12/4)
                            = 108
                          I = bh³ / 12
                            = (6*12³)/12
                            =  864
                         b = 6

             ∴   τ =(48 * 108) / (864 * 6)
                     = 1 kip/inch²

 Answer: 1 kip/inch²

---