Determine Required Section Modulus Using Bending Stress: The formula for bending stress is: = M m a x S = S M max Rearranging this gives: S = M m a x a l l o w = 14 1 0 3 , Nmm 8.27 1 0 6 , N/m 2 = 14 1 0 3 8.27 = 1.69 , cm 3 S= allow M max = 8.2710 6 ,N/m 2 1410 3 ,Nmm = 8.27 1410 3 =1.69,cm 3 Determine Required Area for Shear: The shear stress is given by: = V A d = Ad V Rearranging gives: A = V d A= V d Since d = 3 b d=3b and V = 5 , KN = 5000 , N V=5,KN=5000,N: A = 5000 0.70 d A= 0.70d 5000 Use b b and d d Relationship: Assume b = b b=b and d = 3 b d=3b. The area of the beam's cross-section is given by: A = b d = b 3 b = 3 b 2 A=bd=b3b=3b 2 Substitute into the shear equation: 3 b 2 = 5000 0.70 3 b 3b 2 = 0.703b 5000 Solving this results in: 3 b 3 = 5000 2.1 b 3 = 5000 6.3 793.65 b 9.13 , cm 3b 3 = 2.1 5000 b 3 = 6.3 5000 793.65b9.13,cm Calculate d d: Now substituting b b back in to find d d: d = 3 b 3 9.13 = 27.39 , cm d=3b39.13=27.39,cm Thus, the dimensions of the beam section used in design should be approximately: Width b 9.13 , cm b9.13,cm Depth d 27.39 , cm d27.39,cm It's important also to ensure that deflection is within limits. You would check this with the applied formulas, but these values give you a preliminary design. unit mm