V'n'M - makes the V curve jump up by F . 6.) A concentrated...

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Shear force and bending moment diagrams: a better way than Beer and Johnston section 5.3 The Geometric Theorems Approach for Drawing V and M diagrams: Think of the distributed loading intensity as q , positive up (not w, positive down ). Then, 1.) dV/dx = q(x) (the slope of V equals q ), (not the opposite, minus w!) 2.29 ∆ V =h x1 x2 q(x)dx (the change in V is the area under q [from x 1 to x 2 ]), (not the opposite, minus the area under w!) 3.) dM/dx = V(x) (the slope of M equals V ), 4.29 ∆ M =h x1 x2 V(x)dx (the change in M is the area under V [from x 1 to x 2 ]). Concentrated forces and couples: (Jumps) (not even mentioned in Beer and Johnston!) 5.) A concentrated upward force F
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Unformatted text preview: makes the V curve jump up by F . 6.) A concentrated clockwise couple C makes the M curve jump up by C . (note clockwise ) Using these six facts for plotting V and M diagrams (2 slope theorems, 2 area/change theorems and 2 jump theorems) makes it quick and easy. Generally, the slopes guide the shapes and the changes/jumps determine values of key points. No equations need to be found. If equations for V(x) and M(x) are needed, the fbd of length x (Section 5.2) method is appropriate. However, you should cross out page 314! Page 315 is a much better example of the fbd of length x method for obtaining equations....
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