CIVIL ENGINEERING FORMULAS

Atx: when x < a

Atx: when x > a

Atx: when x > a

Atx: when x = a = 0.414L

Atx: when x < a

Atx: when x > a

Atx: when x < a

At point of load:

At fixed end:

V = R

V = R – W

R 1 = W^3 aL

(^2) – a 3
2 L^3
1
6 EI
R = W^3 b
(^2) L – b 3
2 L^3
3 RL^2 x – Rx^3 –
R 1 (2L^3 – 3L^2 x + x^3 ) –
3 b^2 L – b^3
2 L^3
a
x
W
L
D
R 1
M 1
M
V
b
R
M(max) = Wa D(max) = 0.0098
D=
1
6 EI
D=
3 b^2 L – b^3
2 L^3
M=Wx
3 b^2 L – b^3
2 L^3
M=Wx
3 b^2 L – b^3
2 L^3
WL^3
EI
M 1 (max) = WL –W(L–a)

• W(x–a)

CASE 9. Beam Fixed at One End, Supported at Other—Concentrated Load at Any Point

3 W (L–a)^2 x

3 Wa (L–x)^2

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