Page 71 - Civil Engineering Formulas

L P (l – k)L kL c 1 k < 2 R 2 = Pk R 1 = (l – k)P L wb (2c + b) R 2 = 2L Load Load R 1 R 1 – w (x – a) R 2 Shear R 2 x′L x″L (x′ < k) (x″ < (1 – k)) Shear R 1 x′ L R 2 x″ L k(1 – k)PL Moment PL 3 d max PL 3 3 1 – k 2 = k 2 (1 – k) 2 k 2 3EI
b R 2 1
(2c + b) R 1 w 2 (x – a) w R 1 a – R x
w wb 2L x (a < x < a + b) a + R 1 x′
a
R = (x′ < a) x′ and deflections for a concentrated load at any point of a simply supported prismatic beam.
R 1 ported prismatic beam. (b) Shears and moments for uniform load over part of a

R
wL 2
R =
L 2 wL 2
– xwL 8 5wL 4 384EI Elastic curve
Load Shear Moment L c
L 1 2 (a)
w
wL 4 24EI
1 2
wL 2 xL 1 2 x(l – x)wL 2
R = x < wL 3 24EI x(l – 2x 2 + x 3 ) FIGURE 2.3
R 1 2

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