CIVIL ENGINEERING FORMULAS

FIGURE 2.2 (Continued)

25

CASE 6. Beam Fixed Both Ends—Concentrated Load at Any Point

b^2 (3a + b)

L^3

V (max) = Rwhena < b

=R 1 whena > b

Atx: when x =

whenx < a

Atx: when x < a

At supportR:

At supportR 1 :

Atx:

At point of load:

R 1 = W

R = W M

1 = – W

V = R

a^2 (3b + a)

L^3

ab^2

L^2

anda>b

2 aL

3 a+b

2 Wa^3 b^2

3 EI(3a+b)^2

a

x

W

L

D

R 1

M 1

M 2

M

V

b

R

max neg. mom.

whenb > a

M 2 = – W

a^2 b

L^2

M(max) = Ra+M 1 =Ra – W

D(max) =

Wb^2 x^2

6 EIL^3

D=( 3 aL– 3ax–bx)

M=Rx–W

ab^2

L^2

ab^2

L^2

max neg. mom.

whena > b