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Shear & Moment Diagrams- Cont.

Problem 7-75 Draw the shear and moment diagrams for the beam. Shear & Moment Diagrams- Cont. 8 kN. 15 kN/m. 20 kN.m. 2m. 3m. 2m. 1m. Support reactions: ∑M B = 0 : Ay =-14.3 kN = 14.3 kN ∑F y = 0 : By = 67.3 kN

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Shear & Moment Diagrams- Cont.

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  1. Problem 7-75 Draw the shear and moment diagrams for the beam. Shear & Moment Diagrams- Cont. 8 kN 15 kN/m 20 kN.m 2m 3m 2m 1m

  2. Support reactions: ∑MB = 0 : Ay =-14.3 kN = 14.3 kN ∑Fy = 0 : By = 67.3 kN We need 3 sections to derive the shear eqs: 0 < x < 2, 2- 2 <x< 5 and 5< x< 8 We need 4 sections to derive the moment eqs: 0 < x < 2, 2 < x < 3, 3 <x< 5 and 5< x< 8 8 kN 15 kN/m 20 kN.m Problem 7-75 1m 3m 2m 2m 8kN 15kN/m 20kN.m 14.3kN 67.3kN 4 1 2 3

  3. 8kN 0 < x < 2 ∑Fy = 0 : -14.3 – V = 0 V = -14.3 kN V(0) = V(2) = -14.3 kN ∑M = 0 : 14.3 x + M = 0 M = -14.3 x kN.m M(0) = 0 kN.m M(2) = -28.6 kN.m (Just before x =2) 15kN/m 20kN.m Problem 7-75 67.3kN 14.3kN M 14.3kN V 45 V(kN) x -14.3 M(kN.m) -28.6

  4. 8kN 2 < x < 3 ∑Fy = 0 : -14.3 – V = 0 V = -14.3 kN V(2) = -14.3 kN V(3) = -14.3 kN (just before x = 3) ∑M = 0 : 14.3 x -20 + M = 0 M = 20 -14.3 x kN.m M(2) = -8.6 kN.m (just after x=2) M(3) = -22.9 kN.m 15kN/m 20kN.m Problem 7-75 67.3kN 14.3kN M 14.3kN V 45 V(kN) x -14.3 -8.6 M(kN.m) -28.6 -22.9

  5. 8kN 15kN/m 20kN.m 3 < x < 5 ∑Fy = 0 : -14.3 -8 -+67.V = 0 V = -22.3 kN V(3) = -22.3 kN (just after x=3) V(5) = -22.3 kN (just before x = 5) ∑M = 0 : 14.3 x -20+8(x-3)+M=0 M = -44+22.3x kN.m M(3) = -22.9 kN.m M(5) = -67.5 kN.m 14.3kN 67.3kN Problem 7-75 M V V(kN) x -14.3 -22.3 x -8.6 -28.6 M(kN.m) -22.9 -67.5

  6. 8kN 15kN/m 20kN.m 5 < x < 8 ∑Fy = 0 : -14.3 -8 +67.3-15(x-5)-V = 0 V =120-15x kN V(5) = 45 kN (just after x=5) V(8) = 0 ∑M=0: 14.3 x -20+8(x-3) -67.3(x-5)+15(x-5)(x-5)/2+M=0 M =-7.5(x-8)2 kN.m M(5) = -67.5 kN.m M(8) = 0 kN.m 14.3kN 67.3kN Problem 7-75 15(x-5) M V 45 V(kN) x -14.3 -22.3 x -8.6 M(kN.m) -28.6 -22.9 -67.5

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