Formulas vigas isostaticas
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS For Various Static Loading Conditions
For meaning of symbols, see page 4-187 18. CANTILEVER BEAM—LOAD INCREASING UNIFORMLY TO FIXED END
Total Equiv. Uniform Load . . . . . . . . = W
l
8 3
R=V . . . . . . . . . . . . . . . . . . . =W Vx
W R
x
. . . . . . . . . . . . . . . . . . . =W
Wl 3
x2 l2
M max (at fixedend) . . . . . . . . . . . . =
V
Shear
Mx
M max
. . . . . . . . . . . . . . . . . . . =
Wx 3 3l2 Wl 3 15EI W 60EIl2 (x5 − 5l4 x + 4l5 )
Moment
∆ max (at free end) . . . . . . . . . . . . . = ∆x
. . . . . . . . . . . . . . . . . . . =
19. CANTILEVER BEAM—UNIFORMLY DISTRIBUTED LOAD
l
Total Equiv. Uniform Load . . . . . . . . = 4wl
R = V . . . . . . . . . . . . . . . . .. . = wl
R
wl
Vx
. . . . . . . . . . . . . . . . . . . = wx
wl 2 2 wx 2 2 wl 4 8EI w (x 4 − 4l3 x + 3l4 ) 24EI
x
M max (at fixed end) . . . . . . . . . . . . =
V
Shear
Mx
. . . . . . . . . . . . . . . . . . . =
Moment
M max
∆ max (at free end) . . . . . . . . . . . . . = ∆x
. . . . . . . . . . . . . . . . . . . =
20. BEAM FIXED AT ONE END, FREE TO DEFLECTVERTICALLY BUT NOT ROTATE AT OTHER—UNIFORMLY DISTRIBUTED LOAD
Total Equiv. Uniform Load . . . . . . . . =
l
8 wl 3
wl M R
x
R = V . . . . . . . . . . . . . . . . . . . = wl Vx
. . . . . . . . . . . . . . . . . . . = wx
wl 2 3 w 2 (l − 3x2 ) 6 wl 4 24EI w(l2 − x2 )2 24EI
M max (at fixed end) . . . . . . . . . . . . =
Shear
.4227 l
M1
Moment
V
Mx
. . . . . . . . . . .. . . . . . . . =
∆ max (at deflected end) . . . . . . . . . . =
M max
∆x
. . . . . . . . . . . . . . . . . . . =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM DIAGRAMS AND FORMULAS
4 - 197
BEAM DIAGRAMS AND FORMULAS For Various Static Loading Conditions
For meaning of symbols, see page 4-187 21. CANTILEVER BEAM—CONCENTRATED LOAD AT ANY POINT
Total Equiv. Uniform Load . .. . . . . . =
R=V
l
8Pb l
. . . . . . . . . . . . . . . . . . . =P
x
P
R
M max (at fixed end) . . . . . . . . . . . . = Pb Mx
(when x > a) . . . . . . . . . . . . = P(x − a)
Pb 2 (3l − b) 6EI Pb 3 3EI Pb 2 (3l − 3x − b) 6EI P(l − x)2 (3b − l + x) 6EI
a
b
V
Shear
∆ max (at free end) . . . . . . . . . . . . . = ∆a
(at point of load) . . . . . . . . . . = (when x< a) . . . . . . . . . . . . = (when x > a) . . . . . . . . . . . . =
Moment
Mmax
∆x ∆x
22. CANTILEVER BEAM—CONCENTRATED LOAD AT FREE END
l
Total Equiv. Uniform Load . . . . . . . . = 8P
R=V
P
. . . . . . . . . . . . . . . . . . . =P
x
R
M max (at fixed end) . . . . . . . . . . . . = Pl
V
Mx
. . . . . . . . . . . . . . . . . . . = Px
Pl 3 3EI P (2l3 − 3l2x +x3 ) 6EI
Shear
∆ max (at free end) . . . . . . . . . . . . . =
M max
Moment
∆x
. . . . . . . . . . . . . . . . . . . =
23. BEAM FIXED AT ONE END, FREE TO DEFLECT VERTICALLY BUT NOT ROTATE AT OTHER—CONCENTRATED LOAD AT DEFLECTED END
l
Total Equiv. Uniform Load . . . . . . . . = 4P
R=V
P M
x
. . . . . . . . . . . . . . . . . . . =P
Pl 2 l 2
3
R
M max (atboth ends) . . . . . . . . . . . . =
V
Mx
. . . . . . . . . . . . . . . . . . . = P − x
pl 12EI P(l − x)2 (l + 2x) 12EI
Shear
M max
l 2
∆ max (at deflected end) . . . . . . . . . . =
M max
Moment
∆x
. . . . . . . . . . . . . . . . . . . =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 198
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS For VariousStatic Loading Conditions
For meaning of symbols, see page 4-187 24. BEAM OVERHANGING ONE SUPPORT—UNIFORMLY DISTRIBUTED LOAD
R 1 = V1 . . . . . . . . . . . . . . = R 2 = V2 + V3 . . . . . . . . . . . =
l
w 2 (l − a2 ) 2l w (l + a)2 2l w 2 (l + a2 ) 2l
x
w(l +a)
a x1
V2 V3 Vx
. . . . . . . . . . . . . . . = wa . . . . . . . . . . . . . . . =
R1
V1
a2 l 1 – 2) 2 ( l
R2...
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