Question

assume with values and need proper working solutions

3. Determine the lightest required UB cross-section, for the laterally restrained simply supported beam shown in Figure 3. The beam AB belongs to an accessible roof of an office building. The beam is loaded by a permanent load g = 3kN/m, a uniformly distributed live load p = 5kN/m and snow loads = 2kN/m. Steel grade S235. Produce a complete design of the proposed size of UB. s= 2 kN/ mm...mmm...mmm...mmmm P = 5 kN/m II g= 3 kN/ mm А, I=7.50 m B गरपन Figure 3

Answer 1

Title - Flexural Formula

Solution S235. Given: Material : Steel Grade from standard data book, Youngs Modulus of Elasticity for the steel Grade 5235 E 210 Gla. 2 S = 2 kN/m 2 X 7.50 = 15 kn p 5 kN/m 5 x 7.50 = 37.5 KN 9 3 kN/m 3 X 7.50 = 22.5 KN = 7.50 m २ cross- oy 235 MPa Now to design the lightest required UB section we will have to solve using Euler Beam's ie. Bending / flexural formula. Flexural formula, Mmax E gy y wla INA we To find the marrimum Bending moment (Mmas), have to solve the beam for the support reactions and correspondingly calculate the Bending moment value. CS Maximum CamScanner

2 15+ 37.5 + 22:5. 75 KN 1 S = 2 kN/m = 2x7.5 = 15 KN 1 P = 5 kn/m= 5x7.5 = 37.5kp 9 = 3 kN/m = 3 X 7.5 = 22:5 KN - A B 7777 HA Ho VA VB {(stp+g) = 75 kN , which will act at the center of the beam in downward direction. Cire. at l 7.5m) 2 2 By static Equilibrium conditions, E Fx = 0, HA Ho 2 Fy=0, VA - (s +p+9) + Ve = 0 :: VA - 75 t VB .. VA + VB = 75 EMA = 0, - VB x 7.5 = 0 75 x 7.5 2 7. .: VB - 37.5 kN CS Vard3755 KN CamScanner

2 Maximum Bending moment, Mmax will act at the centre of the Beam, "Mmax 37.5 x 7.5 140.625 kN-m 2 Mmax 140.625 X 106 N-mm substitute values in flexural formula, Mmax бу INA y mman INA oy У Zxx where Z= section modulus Mmax gy > 140.625 X 100 = 235 3 Zat 598.40 x 10" mm Hence Universal Beam having its section modules with respect to -anis equal to 598.40 x 103 mm² will be the lightest beam to successfully support the CSgirem koading condition. CamScanner

Summary - The flexural formula is used to determine the bending stress of the beam. Section modulus determines the lightest size of the section that is required to withstand the bending moment imposed on the beam.