4 - 192
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS For Various Static Loading Conditions For meaning of symbols, see page 4-187 7. SIMPLE BEAM—CONCENTRATED LOAD AT CENTER Total Equiv. Uniform Load . . . . . . . . . . = 2P
l P
x
R
l 2
R=V
. . . . . . . . . . . . . . . . . . . . =
P 2
M max
(at point of load) . . . . . . . . . . . =
Pl 4
Mx
Px 1 when x < . . . . . . . . . . . . . = 2 2
∆ max
(at point of load) . . . . . . . . . . . =
∆x
1 Px (3l2 − 4x2 ) when x < . . . . . . . . . . . . . = 2 48EI
R
l 2
V
Shear
V
M max
Moment
Pl 3 48EI
8. SIMPLE BEAM—CONCENTRATED LOAD AT ANY POINT Total Equiv. Uniform Load . . . . . . . . . . =
l x
P
R
1
a
Pb l
R 2 = V2 (max when a > b ) . . . . . . . . . . . =
Pa l
M max
(at point of load) . . . . . . . . . . . =
Pab l
Mx
(when x < a ) . . . . . . . . . . . . . . =
Pbx l
∆ max
at x =
Pab (a + 2b)√ 3a(a + 2b) 27EIl
∆a
(at point of load) . . . . . . . . . . . =
Pa 2b 2 3EIl
∆x
(when x < a ) . . . . . . . . . . . . . . =
Pbx 2 (l − b 2 − x2 ) 6EIl
V1
V2 Shear
M max
Moment
l2
R 1 = V1 (max when a < b ) . . . . . . . . . . . =
R2
b
8Pab
a(a + 2b) √ when a > b 3
. . . =
9. SIMPLE BEAM—TWO EQUAL CONCENTRATED LOADS SYMMETRICALLY PLACED Total Equiv. Uniform Load . . . . . . . . . . =
l x
P
P
R
R
a
a
V
Shear
V
M max
Moment
8Pa l
R=V
. . . . . . . . . . . . . . . . . . . . =P
M max
(between loads) . . . . . . . . . . . . = Pa
Mx
(when x < a ) . . . . . . . . . . . . . . = Px
∆ max
(at center) . . . . . . . . . . . . . . . =
Pa (3l2 − 4a2 ) 24EI
∆x
(when x < a ) . . . . . . . . . . . . . . =
Px (3la − 3a 2 − x2 ) 6EI
∆x
(when x > a and < (l − a)) . . . . . . . =
Pa (3lx − 3x2 − a 2) 6EI
AMERICAN INSTITUTE OF STEEL CONSTRUCTION