Page 309 - Civil Engineering Formulas

BUILDING AND STRUCTURES FORMULAS 243

W
a b M 1 M 2

b 3
M 1 3 M 2 W
2
2 H a 1 H 2
1
H H 1
V 2
V
V
V 1
FIGURE 9.13 Fixed supports, con- FIGURE 9.14 Fixed supports, concen-
centrated load on horizontal member. trated load on one vertical member.
(Roark–Formulas for Stress and (Roark–Formulas for Stress and Strain,
Strain, McGraw-Hill.) McGraw-Hill.)

With fixed supports and a concentrated load on the horizontal member,
Fig. 9.13:
1 3 1 2 1 3 1 2
3 HL 1 2 M 1 L 1 3 HL 2 2 M 2 L 2 (9.121)
I 1 I 1 I 2 I 2
1 2 1 1 W(bL 3 b /L 3 ) 1
3
2 HL 1 M 1 L 1 3 M 1 L 3 6 6 M 2 L 3 (9.122)
I 1 I 1 I 3 I 3 I 3
1 2 1 1 1 W[2bL 3 (b /L 3 ) 3b ]
3
2
2 HL 2 M 2 L 2 3 M 2 L 3 6 M 1 L 3 6
(9.123)
I 2 I 2 I 3 I 3 I 3
With fixed supports and and a concentrated load on one vertical member,
Fig. 9.14:
1 Wa 3 1 Wa b 1 3 1 2 1 3 1 2
2
3 2 3 H 2 L 1 2 M 1 L 1 3 H 2 L 2 2 M 2 L 2
(9.124)
I 1 I 1 I 1 I 1 I 2 I 2
1 Wa 2 1 2 1 1
2 2 H 2 L 1 M 1 L 1 3 M 1 L 3 6 M 2 L 3 (9.125)
I 1 I 1 I 1 I 3 I 3
1 2 1 1
2 HL 2 M 2 L 2 3 M 2 L 3 6 M 1 L 3
(9.126)
I 2 I 2 I 3 I 3
With fixed supports and a uniform load on the horizontal member, Fig. 9.15:
1 2 1 3 1 3 1 2
2 M 1 L 1 3 HL 1 3 HL 2 2 M 2 L 2 (9.127)
I 1 I 1 I 2 I 2
1 2 1 1 1 2
HL 1 M 1 L 1 M 1 L 3 6 M 2 L 3 24 WL 3
2
3
(9.128)
I 1 I 1 I 3 I 3 I 3
1 2 1 1 1 2
2 HL 2 M 2 L 2 3 M 2 L 3 6 M 1 L 3 24 WL 3 (9.129)
I 2 I 2 I 3 I 3 I 3