Chapter 4 Shear Forces and Bending Moments

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4.5 Shear-Force and Bending-Moment Diagramsconcentrated loadsconsider a simply support beam ABwith a concentrated load PR A = P b / L R B = P a / Lfor 0 < x < aV = R A = P b / LM = R A x = P b x / Lnote that dM / dx = P b / L = Vfora < x < LV = R A - P = - P a / LM = R A x - P (x - a) = P a (L - x) / Lnote that dM / dx = - P a / L = VwithM max = P a b / Luniform loadconsider a simple beam AB with auniformly distributed load of constantintensity q8
R A = R B = q L / 2V = R A - q x = q L / 2 - q xM = R A x - q x (x/2) = q L x / 2 - q x 2 / 2note thatdM / dx = q L / 2 - q x / 2 = VM max = q L 2 / 8 at x = L / 2several concentrated loadsfor 0 < x < a 1 V = R A M = R A xM 1 = R A a 1for a 1 < x < a 2 V = R A - P 1M = R A x - P 1 (x - a 1 )M 2 - M 1 = (R A - P 1 )(a 2 - a 1 )similarly for othersM 2 = M max because V = 0 at that pointExample 4-4construct the shear-force and bending-moment diagrams for the simple beamABR A = q b (b + 2c) / 2LR B = q b (b + 2a) / 2Lfor 0 < x < aV = R AM = R A x9
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Page 7: concentrated loadsequilibrium of fo
Page 11 and 12: Example 4-6construct the V- and M-d

Chapter 4 Shear Forces and Bending Moments

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