Beam Analysis PDF

## EECQ 2151 THEORY OF STRUCTURES IA ### Example 1 A beam ABCD shown in the figure below is simply supported at B and C. It carries a point load at the free end A of 60KN, a uniformly distributed load between B and C of 60Kn/m and an anti-clockwise moment of in the plane of the beam at free end D...

## EECQ 2151 THEORY OF STRUCTURES IA ### Example 1 A beam ABCD shown in the figure below is simply supported at B and C. It carries a point load at the free end A of 60KN, a uniformly distributed load between B and C of 60Kn/m and an anti-clockwise moment of in the plane of the beam at free end D of 80kNm sketch the SFD and BMD indicating values at all points. ![Diagram of the beam with various forces and dimensions annotated.] * **SFD:** - $SF_A = R_A = -60KN$ - $SF_{A-B}$ = Constant - $SF_{B-C} = -60 + 230 = 170KN$ - $SF_{C-D} = 170 - (60 \times 4) = -70KN$ - $SF_{D} = -70 +70 = 0$ * **BMD:** - $BM_A = 0$ - $BM_B = -60\times2 = -120$ - $BM_{B'} = -60 \times 4.8 + 230 \times 2.8 - 60 \times 2.8 \times 2.8 = 120.8 KN m $ - $BM_C = 60 \times 6 + 230 \times 4 - 60 \times 7 \times 4/2 = 80KNm$ ### Example 2 Draw the shear and bending moment diagrams for the beam shown in Fig below. ![Diagram of the beam with various forces and dimensions annotated.] * **SFD:** - $R_{Bv} = 250$ - $R_{Cv} = 177.404$ * **BMD:** - $BM_A = 0$ - $BM_B = -90 \times 6.5 + 13 \times 4 - 45 \times 6.5 \times 6.5^2 + 45 \times [6.5]^2 + R_{Bv} \times 6.5 = 0$ - $BM_C = 60 \times 6 + 230 \times 4 - 60 \times 7 \times 4/2 = 80KNm$