CIVIL ENGINEERING FORMULAS

23

FIGURE 2.2 (Continued)

CASE 4. Beam Supported Both Ends—Three Unequal Concentrated Loads, Unequally Distributed

R =

Wb + W 1 b 1 + W 2 b 2

L

R 1 =

V (max) = Maximum reaction

Atx: when x > a and < a 1

Atx: when x = a

Atx: when x = a 1

M = Ra

M 1 = Ra 1 – W (a 1 – a)

Atx: when x = a 2

M 2 = Ra 2 – W (a 2 – a) – W 1 (a 2 – a 1 )

M (max) = M when W = R or > R

M (max) = M 1 when

M (max) = M 2 when W 2 = R 1 or > R 1

L

a 2

W W 1 W 2

R

M

V

x

R 1

M 1

M 2

b 2

b 1

a b

W 1 + W = R or > R

Atx: when x > a 1 and < a (^2) W 1 + W 2 = R 1 or > R 1
V = R – W
V = R – W – W 1
Wa + W 1 a 1 + W 2 a 2
L
a 1