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Page 20 - ZSi-Foster Engineering Catalog - Electronic Version 2
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``````Beam Load Support Formulas
Cantilever Beams
P aPb
V max. = P V max. = W V max. = P
L M max. = PL L M max. =WL L M max. = Pb 3232
max. = PL max. = WL
3EI V 8EI V
max. = Pb (3L-b) 6EI
V MMM
Simple Beams
L2P aPb R= P R= W
R1= Pb L2PL2WLL
R V
M
R1 V
M
V
V max. = R
R V max. = R R
P2L W2L1 LPa
R2 R2= Pa
V max. = L
M max. = 4
V M
M max. = 8
V M
max. = PL3 48EI
max. = 5WL3 384EI
M max. =Pab L
max. = Pab(a+2b) 3a(a+2b) 27EIL
L2 P
Beams Fixed At One End & Supported At The Other
a
Pb R=Pb2(a+2L) 1 2L3
R1=5P
R1=3W
L 1611P L 85W L Pa22
V max. = 16 R1 V max. = 8 R1
R2
R2=2L3(3L -a )
M at point of load = R1a
M at fixed end = Pab (a+L)
M max. =3PL V 16
max. at x = 0.447L
max. = 0.009317PL3 M EI
V max. = P2
M max. =WL V
3L8 8
max. at x = 0.4215L
3L max. = WL3 M 4 185EI
Beams Fixed At Both Ends
2L3
L2 P L
Pb
123 R1 R22L3
V max. = W2 M max. =WL
a
R=Pb2(3a+b) 1 L3
M max. =PL 83
L
L
R =Pa2(a+3b)
max. = PL 192EI
V
max. = WL V 384EI
M = Pab2 1 L2
– Deflection
E – Modulus of Elasticity I – Moment of Inertia
M =Pa2b
M M MM2L2 12
R – Reaction
M – Moment
W – Total Uniform Load V – Shear
L – Length
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