Page 54 - Civil Engineering Formulas
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CASE 4. Beam Supported Both Ends—Three Unequal Concentrated Loads, Unequally Distributed
M 1 = Ra 1 – W (a 1 – a) W 1 + W = R or > R W 1 + W 2 = R 1 or > R 1 b 2 W 2 R 1 M 1 M 2
M = Ra M 2 = Ra 2 – W (a 2 – a) – W 1 (a 2 – a 1 ) M (max) = M when W = R or > R M (max) = M 2 when W 2 = R 1 or > R 1 L b 1 W 1 b
x: when x = a x: when x = a 1 x: when x = a 2 M (max) = M 1 when a 2 a 1 W a x
At At At R M V
Wb + W 1 b 1 + W 2 b 2 L Wa + W 1 a 1 + W 2 a 2 L V = R – W V = R – W – W 1
R = R 1 = V (max) = Maximum reaction x: when x > a and < a 1 At x: when x > a 1 and < a 2 At (Continued) FIGURE 2.2
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