Question

A wooden beam is reinforced with steel located on the bottom side as shown below. Determine the normal stress at points B and C when E. = 12 GPa and Es = 200 GP.|| 150 mm . M-2XN-m 150 mm 20 mm

Answer 1

Solution. Isomm B Ew=12 Gpa, Est=200 Gpa Bending wood 150mm Moment 2 KN-m 20 min steel steps: converting the whole section into wooden Section Modular ratio Ew 3 width of equivalent wood section for steel m xiso = = 2500 mm Sexle = 25000 20x10 + (1soxiso) xgS 36.38 mm 2 Soox20+ ISOX ISO isomm 133.62 mm ww asl 139.62 ý = 36.38mm zom - 2500mm Equivalent wooden section of wooden section 2500x28(2500*20) x (26-38) + 150x (1503 + (150x150) (58.62) Ier = 155.966 x 106 mm Jer

Step 2: Bending stress 11 MY M - 2KN-ro At Top i.e point B, Y = 133.62 mm So, 2 x 10 x 133.62 iss. g66x106 1-7134 N/mm². so, maninum Bending point "B" is 1.7134 N/mm². Stress in wood is top Step3 now, Now, Bending stress at point c [bottom equivalent wood section] 6 60 му 2x 10 x 36.38 i55.966 x 100 =0.4665 N/mm² extreme c = 0.4 665 is maximum stress at Fiber of equivalent wooden section, but in actual no wood is there. So corresponding stress in sted will be manimum at this location. By strain compatibility equiv. Wooden section ). steel Sc) max man Es steel Oman +(59)x 0.4665 = 7.775 N/mm² So, normal stress at point is 7.775 N/mm² and at point B is 1.7134 N/mm²