CIVIL ENGINEERING FORMULAS

35

Load

Shear

Moment

Elastic curve

(j)

R = wL

wLx

wL

xL

L

w

wL^2

2

wL^2

2

(3 – 4x + x^4 )

x^2

wL^4

24 EI

wL^4

8 EI

(^12) wL 2
Load
Shear
Moment
Elastic curve
(k)
R 1 =
R 2
R 1
wL′
wL′x′
x′L′
xL
LL′ w
wL′^2
2 LR^2 =
wL′
2 L
wL′^2
2
L
3
(4L + 3L′)
x(1 – x^2 )
x′^2
wL′^3
24 EI
dmax =
wL′^2 L^2
wL′^2 L^2
12 EI
(^1) wL′ (^2) x
2
(^1) wL′ 2
2
(^183) EI
(2L + L′)
Load
Shear
Moment
Elastic curve
(l)
R = W
w
W =
Wx^2
W
xL
xL
L
wx
WL
3
L
3
WL
3
wL
2
WL
3
(4 – 5x + x^3 )
x^3
WL^3
60 EI
WL^3
15 EI
FIGURE 2.3 Elastic-curve equations for prismatic beams: (j) Shears, moments, and deflections for uniform load over the full length of a cantilever.
(k) Shears, moments, and deflections for uniform load on a beam overhang. (l) Shears, moments, and deflections for triangular loading on a prismatic
cantilever. (Continued)