Page 36 - ZSi-Foster Product Catalog

Beam Load Support Formulas

Cantilever Beams

P P
a b
V max. = P V max. = W V max. = P
L L WL L
M max. = PL M max. = M max. = Pb
2
2
PL 3 WL 3 Pb (3L-b)
max. = max. = max. =
3EI V 8EI V 6EI
V
M M M

Simple Beams

P P
L
2 P W a b
R= R= R = Pb
2 2 1 L
L P L W L Pa
R R V max. = R R V max. = R R R =
2 2 1 2 2 L
V M max. = PL V M max. = WL V V max. = Pa
4 8 L
PL 3 5WL 3 Pab
max. = max. = M max. =
48EI 384EI L
Pab(a+2b) 3a(a+2b)
M M M max. = 27EIL
Beams Fixed At One End & Supported At The Other
P P
L Pb 2
2 5P 3W a b R = 3 (a+2L)
1
R = R = 2L
1 16 1 8
L L L
2 2
R V max. = 11P V max. = 5W R = Pa (3L -a )
1 16 R 1 8 R 1 R 2 2 2L 3
V M max. = 3PL V M max. = WL V
16 8 M at point of load = R a
3L 1
8
max. at x = 0.447L max. at x = 0.4215L
Pab
M at fixed end = 3 (a+L)
3
M PL 3 M max. = WL M 2L
max. = 0.009317 3L 185EI
EI 4
Beams Fixed At Both Ends
P P
L 2
2 P W a b R = Pb (3a+b)
V max. = V max. = 1 L 3
2 2
L PL L WL L 2
M max. = M max. = R = Pa (a+3b)
8 12 R 1 R 2 2 L 3
V max. = PL 3 V max. = WL 3 V
192EI 384EI 2
M = Pab
1 2
L
2
M = Pa b
2 2
L
M M M M
1 2
R – Reaction W – Total Uniform Load – Deflection
M – Moment V – Shear E – Modulus of Elasticity
P – Concentrated Load L – Length I – Moment of Inertia
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