Page 64 - Civil Engineering Formulas

WL 3 EI x W (L – R1(2L 3 – 3L 2 x + x 3 ) – 2 x) Wa (L – 3
x: when x = a = 0.414L (max) = 0.0098 D x: when x < a 1 3RL 2 x – Rx 3 – a) 2 3 6EI x: when x > a 1 6EI

CASE 9. Beam Fixed at One End, Supported at Other—Concentrated Load at Any Point
At At = D At = D

a) a)
– –
(L (x W M M1
3b 2 L – b 3 2L 3 W – 3b 2 L – b 3 2L 3 3b 2 L – b 3 – 2L 3 R1

(max) = Wa 3b 2 L – b 3 2L 3 Wx = M Wx = L W b a x

At point of load: M At fixed end: (max) = WL M 1 x: when x < a At x: when x > a At M D R V

3b 2 L – b 3 2L 3 3aL 2 – a 3 2L 3 V = R V = R – W

R = W R 1 = W x: when x < a x: when x > a

At At

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