Page 58 - Civil Engineering Formulas
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bx)
b
> b) 2 –
a + – 3ax
and Wa 3 b 2 (3a
b (3aL
aL + 2 EI
3a x < a Wb 2 x 2 EIL 3
2 3
x: when x = (max) = D when = D 6
At
CASE 6. Beam Fixed Both Ends—Concentrated Load at Any Point
ab 2 L 2 a 2 b L 2 ab 2 L 2 D M M 2 V
= – W = – W Ra – W M 1 = ab 2 L 2 W b R 1
R: max neg. mom. b > a when R 1: max neg. mom. a > b when (max) = Ra + W Rx – = L a x
At support M 1 At support M 2 At point of load: M M x: At R M 1
a < b a > b
b 2 (3a + b) L 3 a 2 (3b + a) L 3 when when R 1 = V = R (Continued)
R = W R 1 = W V (max) = R x: when x < a FIGURE 2.2
At
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