Formulas vigas isostaticas

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4 - 196

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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