Structural Concrete - Hassoun

1022 Appendix C Structural Aids
Table C.3
Propped Beams
25. Uniform load:
W = total load = wL
R A = V A = 5W R
8 B = V B = 3W 8
M A =− WL M
8 C = 9WL (at x = 3 )
128 8 L
Δ x = WL3
48EI (m − 3m3 + 2m 4 )
Δ max =
WL3
185EI
where m = x L
at a distance x = 0.4215L (from support B)
26. Partial uniform load starting from hinged support:
W = wb
n = b L
R A = V A = Wn
8 (6 − n2 )
R B = V B = W 8 (n3 − 6n + 8)
M A =− Wb
8 (2 − n2 ) M C = Wb
8 (6n − n3 − 4)
Δ x = WbL2
48EI [(n2 − 6)m 3 −(3n 2 − 6)m 2 ]
when x ≤ a
Δ x =
WL4
48bEI [2P4 − p 3 n(n 3 − 6n + 8)+Pn 2 (3n 2 − 8n + 6)]
x ≥ a and P = L − x
L
when
27. Partial uniform load starting from fixed end:
W = wa
n = a L
R A = V A = W 8 [8 − n2 (4 − n)]
R B = V B = Wn2
8 (4 − n) Y = b + an2 (4 − n)
M A =− W a
(2 − n)2
8
{ [
M max = Wa 8 − n 2 (4 − n) ] 2
−
8
16
Δ C = Wa3
48EI (6 − 12n + 7n2 − n 3 )
+ 4 − n(4 − n)
}
(continued)