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Structural Concrete - Hassoun

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Appendix C <strong>Structural</strong> Aids 1025<br />

Table C.4<br />

Fixed-End Beams<br />

33. Uniform load:<br />

W = total load = wL<br />

R A = V A = R B = V B = W 2<br />

M A = M B =− WL (at support)<br />

12<br />

M C max = WL (at midspan)<br />

24<br />

Δ max =<br />

Δ x =<br />

WL3<br />

384EI<br />

(at midspan)<br />

Wx3<br />

24EIL (L − x)2 (from A or B)<br />

34. Uniform partial load at one end:<br />

W = total load = wa<br />

m = a L<br />

R A = V A = W(m3 − 2m 2 + 2)<br />

2<br />

R B = V B = Wm2 (2 − m)<br />

2<br />

M A = WLm<br />

12 (3m2 − 8m + 6)<br />

M B = WLm2 (4 − 3m)<br />

12<br />

M max = WLm2<br />

12<br />

when x = a 2 (m3 − 2m 2 + 2)<br />

Δ max =<br />

Δ C =<br />

WL3<br />

333EI<br />

WL3<br />

384EI<br />

= W − R A<br />

(<br />

− 3 )<br />

2 m5 + 6m 4 − 6m 3 − 6m 2 + 15m − 8

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