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Structural Concrete - Hassoun

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1016 Appendix C <strong>Structural</strong> Aids<br />

Table C.1<br />

(Continued)<br />

7. External moment at any point:<br />

R A =−R B = V A = V B = M L<br />

M CA = Ma<br />

L<br />

M CB = Mb<br />

L<br />

Δ c = −Mab (a − b)<br />

3EIL<br />

8. Concentrated load at midspan:<br />

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

M max = PL<br />

4<br />

Δ max = PL3<br />

48EI<br />

(at midspan)<br />

(at midspan)<br />

9. Concentrated load at any point:<br />

R A = V A = Pb<br />

L<br />

R B = V B = Pa<br />

L<br />

M max = Pab (at point load)<br />

L<br />

Δ c = Pa2 b 2<br />

3EIL<br />

Δ max = PL3<br />

48EI<br />

(at point load)<br />

[ ( ) 3a a 3<br />

]<br />

L − 4 L<br />

(when a ≥ b)<br />

at x = √ a(b + L)∕3<br />

(continued)

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