CIVIL ENGINEERING FORMULAS

BEAM FORMULAS 37

Shear

Moment

(n)

R=V

Mmax(at center)

∆max(at center)

∆x

R

V

R

x W

l

V

Mmax

=(W l^2 – 4x^2 )

2 l^2

=W

2

=

Wl

6

Wx (5l (^2) – 4x (^2) ) 2
480 EIl^2

=

l

2

l

2

Vx

Mx

whenx < l

2

whenx < l =Wx –

2

2 x^2

3 l^2

1

2

= Wl

3

60 EI

Shear

Moment

(o)

R 1 =V1max (2l–a)

Mmax

R 1 R 2

R 1

W V 2

a

wa

x

l

V 1

Mmax

=

wx^2

2

R 2 =V 2

R 1 – wx

=wa

2

2 l

wa

2 l

=

=

wx

24 EIl

=

V (when x < a)

=R 1 x–

=R 2 (l–x)

Mx (when x < a)

Mx (when x > a)

∆x (when x < a) = [a^2 (2l–a)^2

wa^2 (l–x)

24 EIl

(4xl– 2x^2 – a^2 )

∆x (when x > a) =

R 1

w

R 12

2 w

atx

• 2ax^2 (2l–a)+lx^3 ]

FIGURE 2.3 Elastic-curve equations for prismatic beams: (n) Simple beam—load

increasing uniformly to center. (Continued)

FIGURE 2.3 Elastic-curve equations for prismatic beams: (o) Simple beam—uniform

load partially distributed at one end. (Continued)