CIVIL ENGINEERING FORMULAS

FIGURE 2.2 (Continued)

27

D

R 1

V

W

x

ab

L

M

CASE 8. Beam Fixed at One End (Cantilever)—Concentrated Load at Any Point

R 1 = V (max) = W

M (max) = Wb

M = W(x = a)

Atx: when x > a

At fixed end:

At free end:

Atx: when x < a

Atx: when x > a

Atx: when x > a

V = W

V = 0

WL^3

6 EI

3 a 3

L

D(max) = 2 – a

L

+

W

6 EI

–3aL^2 + 2L^3 + x^3

–3ax^2 – 3L^2 x + 6aLx

D=

At point of load:

W

3 EI

D =(L–a)^3