BEAM DIAGRAMS AND FORMULAS
4 - 205
BEAM DIAGRAMS AND FORMULAS Design properties of cantilevered beams Equal loads, equally spaced No. Spans
System a
2
M1 M1
M1
A
B
3
A
b
b
M3
M3
M2
M2
M3
C
D
c
c
C
D
M1
M1 M1
M1
M4
A
E
4
A
E
d
M1 M1
b
D
M1
D M1 M1
A
F
H
f
f
H M3
C M1
M5
H
G
3
F
A
4 P 2
P
P
5 P
P 2
P 2
P
P
P
P
Moments
P
P 2
M1 M2 M3 M4 M5
0.086PL 0.096PL 0.063PL 0.039PL 0.051PL
0.167PL 0.188PL 0.125PL 0.083PL 0.104PL
0.250PL 0.278PL 0.167PL 0.083PL 0.139PL
0.333PL 0.375PL 0.250PL 0.167PL 0.208PL
0.429PL 0.480PL 0.300PL 0.171PL 0.249PL
Reactions
P
D M1
M3
H
M2 d
e
A B C D E F G H
0.414P 1.172P 0.438P 1.063P 1.086P 1.109P 0.977P 1.000P
0.833P 2.333P 0.875P 2.125P 2.167P 2.208P 1.958P 2.000P
1.250P 3.500P 1.333P 3.167P 3.250P 3.333P 2.917P 3.000P
1.667P 4.667P 1.750P 4.250P 4.333P 4.417P 3.917P 4.000P
2.071P 5.857P 2.200P 5.300P 5.429P 5.557P 4.871P 5.000P
Cantilever Dimensions
P
H
M3
P 2
M3 M3
M3
M3
P 2
b
M3 M3
M3
2 P 2
P
C
f
M3
M3
G
∞
D
f
M3
M5
M2
H
M3 H e M3
d
M3 M3
f
M3 M3
b
M3 M3
H
f
M3
A
f
f
M3
G
b
C M1
F
M3
F
D M1
G
M5
M2
d
M5
e M3
M1
C
e
M3
G
d
Typical Span Loading
H
M3
F
M2
M3
H e M3
d
M5
A
b
M3
M3 M3
M1 A
C
f
M3
M3
M1
n
D
f M3
M2 C
M2
G
F
5
≥7 (odd)
M3 M3
M5
A
≥6 (even)
b
e M3
a b c d e f
0.172L 0.125L 0.220L 0.204L 0.157L 0.147L
0.250L 0.200L 0.333L 0.308L 0.273L 0.250L
0.200L 0.143L 0.250L 0.231L 0.182L 0.167L
0.182L 0.143L 0.222L 0.211L 0.176L 0.167L
0.176L 0.130L 0.229L 0.203L 0.160L 0.150L
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
P 2