BEAM DIAGRAMS AND FORMULASDesign properties of cantilevered beams

Equal loads, equally spaced

No. Spans System

2

3

4

5

≥6(even)

≥7(odd)

n ∞∞ 2 3 4 5

Typical SpanLoading

M1

M2

M3

M4

M5

0.086PL0.096PL0.063PL0.039PL0.051PL

0.167PL0.188PL0.125PL0.083PL0.104PL

0.250PL0.278PL0.167PL0.083PL0.139PL

0.333PL0.375PL0.250PL0.167PL0.208PL

0.429PL0.480PL0.300PL0.171PL0.249PL

ABCDEFGH

0.414P1.172P0.438P1.063P1.086P1.109P0.977P1.000P

0.833P2.333P0.875P2.125P2.167P2.208P1.958P2.000P

1.250P3.500P1.333P3.167P3.250P3.333P2.917P3.000P

1.667P4.667P1.750P4.250P4.333P4.417P3.917P4.000P

2.071P5.857P2.200P5.300P5.429P5.557P4.871P5.000P

abcdef

0.172L0.125L0.220L0.204L0.157L0.147L

0.250L0.200L0.333L0.308L0.273L0.250L

0.200L0.143L0.250L0.231L0.182L0.167L

0.182L0.143L0.222L0.211L0.176L0.167L

0.176L0.130L0.229L0.203L0.160L0.150L

Mom

ents

Rea

ctio

nsC

antil

ever

Dim

ensi

ons

1M

1M M1

A B

a

A

M3 3M

1M M1

2M 3M 2M

1M M4 1M

C

A

D

E

D

E

C

A

b b

c c

1M M3 M31M M5 3M 2M

A F G D C

d e b

M3 3M 3M 3M

1M M3 M3 M1

2M 3M 3M 3M 2M

1M M5 3M 5M M1

C

A

D

F

H

G

H

G

D

F

C

A

b f bf

d e e d

f f

1M M3 M3 M3 M31M M5 3M 3M M3 2M

A F G H H D C

d e b

M3 3M 3M 3M 3M 3M

1M M3 M3 M3 M3 M1

2M 3M 3M 3M 3M 3M 2M

1M M5 3M 3M M3 5M 1M

C

A

D

F

H

G

H

H

H

H

H

G

D

F

C

A

b f

f f

f f bf

d e e d

P 2P

2P

P 2P

2P

PP 2P

2P

PP P 2P

2P

PP P P

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

BEAM DIAGRAMS AND FORMULAS 4 - 205