CIVIL ENGINEERING FORMULAS

BEAM FORMULAS 41

kL

kL

kL kL

kL

• k(l–k)^2 WL

k(l–k)WL

k(l–k)WL

k^2 (l–k)WL

W

L

L L

(a) (b)

(c) (d)

w

L

WL

12

WL

12

L

2

WL

W = wL

L

4

L

4

L

4

L

4

1

8

WL

1

8

WL

1

8

WL

1

6

WL

5

48

WL

5

48

W

1

3

1

2

k(l–k)WL

1

2

kWL

1

2

W

2

W

2

W

1

3

W

1

3

–

–

• cL

FIGURE 2.6 Fixed-end moments for a prismatic beam. (a) For a concentrated load.
(b) For a uniform load. (c) For two equal concentrated loads. (d) For three equal
concentrated loads.