Page 78 - Civil Engineering Formulas

(4 – 5x + x 3 ) WL 3 15EI
xL xL

wx Wx 2 WL x 3 3
wL 2 Load Shear WL 3 60EI
W = L Moment Elastic curve (l)

L 3
R = W
w W WL 3
WL 3

(4L + 3L′)

w
x′L′ wL′x′ wL′ 2 x′ 2 2 wL′ 2 24EI
L′ R 2 1 2 x(1 – x 2 ) wL′ 3
(2L + L′) wL′ Elastic-curve equations for prismatic beams: (j) Shears, moments, and deflections for uniform load over the full length of a cantilever.

wL′ 2L Load Shear wL′ 2 L 2 12EI Elastic curve (k) (k) Shears, moments, and deflections for uniform load on a beam overhang. (l) Shears, moments, and deflections for triangular loading on a prismatic
R 2 =
L
R 1 = wL′ 2 2L xL 1 wL′ 2 x 2 Moment L 3 wL′ 2 L 2 3EI

d max = 18
R 1

wL 4 8EI

xL (3 – 4x + x 4 )
L
w Shear wL 2 x 2 2 Moment
Load wL 4 24EI Elastic curve (j)

R = wL wLx cantilever. (Continued)

wL 2 2 wL wL 2 FIGURE 2.3
1 2

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