CIVIL ENGINEERING FORMULAS

44 CHAPTER TWO

W =

wyL

2

yL

xL

yL yL yL yL yL yL

aL

P PPPPPP

yL

xL

• xL

Ldx

xL

yL

y

0

w

Case 6

G^2 =n y^2 =

(^2) – 1
12
n+ 1
n– 1
LÚwx′dx′
W
y
W=LÚ 0 f(x′)dx′
a^2
12
.
S^3 = 0
Case 5
S^3 = 0
Case 7 Case 8
x =
W = nP
y
yL
1
2
x =
x =
y
LÚ 0 wx
(^2) dx
W
G^2 =
y
LÚ 0 wx
(^3) dx
W
S^3 =
n– 1y
2
1
2
(^1) yL
2
G^2 =^1 y^2
24
S^3 = –
x =
x =
(^1) y
4
G^2 =^3 y^2
80
(^1) y 3
160
W =
1
3
wyL
w = ky^2 L^2
W = f(x′)
x′L

FIGURE 2.8 (Continued)