Structural Concrete - Hassoun

Appendix C Structural Aids 1019
Table C.1
(Continued)
16. Concentrated load at center and variable end moments:
R A = V A = P 2 + M 1 − M 2
L
R B = V B = P 2 − M 1 − M 2
L
M 3 = PL
4 − M 1 + M 2
(at midspan)
2
(
P
M x =
2 + M 1 − M )
2
x − M
L
1 when x < L 2
M x = P 2 (L − x)+(M 1 − M 2 ) x − M
L
1 when x > L 2
Δ x =
Px
{
}
3L 2 − 4x 2 8 (L − x)
− [M
48EI
PL 1 (2L − x)+M 2 (L + x)]
whenx < L 2
17. One concentrated moving load:
R A max = V A max = P at x = 0
R B max = V A max = P
M max = PL
4
at x = L 2
at x = L
M x = P (L − x)x
L
18. Two equal concentrated moving loads:
(
R A max = V A max = P 2 − a )
at x = 0
L
M max = P (
L − a ) 2
2L 2
when a < 0.586L under load1at x = 1 (
L − a )
.
2 2
M max = PL
4
when a > 0.5L with one load at midspan.