Formulario de maderas

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BEAM DIAGRAMS AND FORMULAS
For various static loading conditions
For meaning ofsymbols, seepage 2-111.
1.
SIMPLE BEAM-UNIFORMLY DISTRIBUTED LOAD
Total Equiv. Uniform Load R-V Vx M max. ( at center ) Mx - wi

~.

'-""1 .:

BEAM D~GRAMS AND FORMULAS
For various static loading conditions
For meaning ofsymbols, see page 2-lll.

t
4.

.~
2
-wei-x)

1

t
i
;
~

SIMPLEBEAM-UNIFORM LOAD PARTIALLY DiSTRIBUTED

R, = V, Ro = Vo

( max. when a

c) ( max. when a > c)
< > a and < (a + b»)
)

wb = 2T (2c + b) wb =2T(2a+b)
= =
=

1

R\~-I

1'".
Shear

Vx

( when x

R,-w (x-a) R, (a +
RIX

-8
_ ~x (I-x)

wl O

v,llllih' I

I

M max. ( at x

= a + ~1
<

:~)

V2 Mx Mx Mx

e

when x

a)

( when x ( when x

> a and < (a +b») > (a + b») .

= Rtx--'i- (x-a)O = R.(l-x)

L\max. (at center)
~x

- 384Ef'
=

5 wi'

wx 241::1 (I' -- 2i~0 + x')

I
r

----------­

---
'\ i) 1/
2.

----------

I

SIMPLE BEAM-LOAD INCREASING UNIFORMLY TO ONE END
Total Equiv. Uniform Load R, = V, . Ro = Vo max.
= =
=

5.

SIMPLE BEAM-UNIFORM LOAD PARTIALLY DiSTRIBUTED AT ONE END

"

9,3
W T

l~~ =a_

RI

=

VI max.

= ~~ (21-a)
= =

1.0264W

I Ro = Vo Vx (when x < a)

2T"'
R1-wx R,o

wa a

2W -3 ­ W Wx o

Mmax.(atx=
V. M x


V,

=T-II""
2WI - -----c=
9-013
~

e

:1)
<

=

2W""
wxo Ro (I-x)

when x

a)

= R,x- ­ 2­
=

* I' I 1TIJ>..-1'J

I I I

I '"

I M max. ( at x = .,_ = .5n41 ) ,3 Mx arnax.

Mx
.1283 WI j.x .:l.x

(Whenx

> a)

(When x <

= Wx (IO-xO) 31 0

a) (when x> a)

A wx = __ ( a O(21-a)0-2ax 2(21-a)+lx' )
= 24EII wao(l-x) 24EII (4xl- 2. 2
-

a O)

(atx=I~I-'\)!s-.51931)=
=

.01304

~:.
(3x"-101 0xo+71')

~x
3.



~ l80Eli0

6.

SIMPLE BEAM-UNIFORM LOAD PARTIALLY DiSTRIBUTED AT EACH END
R1
=

V,

SIMPLE BEAM-LOAD INCREASING UNIFORMLY TO CENTER
Total Equiv.Uniform Load R-V
=-3­

Ro = Vo

w,a(21-a) +WICo 21 woc(21- c) + w,a o 21

4W

-T
(when x

W

Vx

b)
Rl
=

Vs,(maxo when a

<

= V, = V.
(when x > a and < (1- b»)
(max. when RI < PI)

P, (I-a) + P.b =---1

I~

=j

=

-j

P,a + Pz (1- b) I

M max. ( at point of load)
.' I I ! ! ,

Pab =-1­ Pbx =-1 ­ whena>b) Pab (a + 2b) " 3a (a + 2b) 27 EI I Pa'b'
b2 -

VxV,

= R, - P,

II I I

I I I I I I i

I 'v Mx z
11m ax.

(when x < a

)

I I II It

j

I

M,
M. Mx

= R1. a
= R.b

~

(atx=~a(a~2b)
( at poi nt of load )
(when
x

( max. when R. < P.) (when x < a) (when x > a and < (I-b»)

aa
Moment

.ax

<

a

)

- """"3ETl Pbx =6ETT (I' -

=

R,x

x')

Moment

Mx

= R,x-P , (x-a)

9.

SIMPLEBEAM-TWO EQUAL CONCENTRATED LOADS SYMMETRICALLY PLACED
Total Equiv. Uniform Load
8 Pa *-1­

12.

BEAM FIXED AT ONE END, SUPPORTED AT OTHER ­ UNIFORMLY DISTRIBUTED LOAD
Total Equiv. Uniform Load
Wt

=

wi

l: ' T T

l R

R-V
M max.( between loads) Mx
(When x

-.,%

o//--

R 1 = VI
J -

.

.

-

p

=

tlllllll!1 ! ling R \ ~;%R2

=~ 8
_ 5wl - -8 ­

-V

Pa Px~ v«
MI

z max.

...
(atx =

=
_

Rl-WX

<

a) a)
(1-

=

M max . . .

_. -8­

wl Z

'it
amax.

(at center)

Pa = 24EI (31'-4a') = a»)
=

i

_ I)

9
R1X-

- 128 wi'
wx -2­
2

IIx IIx

e

Mx

.....
=

when x <

6IT (3Ia-3a'-x') 6IT (3Ix-3x' Pa a')

Px

amax. (atx = /6 (1 +"'33) = .42151)

185ET

,J.:" .

( when x > a and
.:1)(..

........•

wx = 48EI (I' - 31x2 + 2x')

AMERICAN

INSTITUTE OF STEEL CONSTRUCTION

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

1

BEAM DIAGRAMS AND FORMULAS For various static loading conditions
For meaning of symbols. see page 2-[[[

'A• . . ,iWst
,.;

BEAM DIAGRAMS AND FORMULAS For various static loading conditions
For meaning 01 symbols. S~ :.~~ 2·:::...
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