Embed Size (px)
Citation preview
-----------------------------------------------------------
+ Exa~k Jt../3
o.
~/j
EXAMPLE 4.13
f.1 , - - - 8 m ------ojThe rigid frame shown is made of the elements of Example 4.8.
1. Using the influence coefficients of Example 4.8 assemble the stiffness equations relating the forces applied at b to the degrees of freedom at that joint.
2. Calculate the displacement at b.
Example 4.13 is a preview of frame analysis problems. Here the emphasis is on the physical interpretation of the stiffness influence coefficients. Note that although in Example 4.13 the nodes are lettered a, b, and e as in Example 4.8 and the member sections correspond, the orientation of member be with respect to the coordinate system is different than it is in Example 4.8. This ad hoc arrangement should cause no difficulty in interpretation of the influence coefficients. But after transformation procedures are introduced in the next chapter, problems of this sort will be solved in a more automatic way.
Sr:',"Y
Boundary conditions:
" -----------------. --+-~~Nonzero degrees of freedom: fay -----x
Ub, Vb and (}zb Rmza Pxb = lOO/,n kN
Rya
____________________________ _________________________________ _
------
-+
,..i',i 13 Element stiffness equations. Use Equation 4.34, omitting out-of-plane shear and bending degrees of freedom, that is, Wl, 8Y l> W2, and 8y2 '
- Memberab
~~ r;~ M~~
M~~ p:~ r;~ M~~
M~Z
Member be
F~g
F~~ M~g
M~~ F~~ F~~ M~~
M~~
+ I. .s -I-i ffnd.!
S ~c-L
= 200
= 200
0.750 o o o -0.750 o o o 0.00469 o 18.750: 0 -0.00469 o 18.750
I
14.423 o : 0 o -14.423 o 1.0 X 105
J: 0 -18.750 0 0.5 x lOs
Sym
0.800 0 0 o 0.00480 0 l2.000
7.692 o
: I
0.750 0
0.00469
0
o 0
-18.750
14.423 0
1.0 X 105
: -0.800 o 0 o 0 -0.00480 0 l2.000 0 o -7.692 o
0.4 x lOs: 0 -l2.000 0 0.2 X 105
----------------------------,-------------------------------- : 0.800 0 0 0
Sym 0.00480 0 -l2.000
7.692 0 0.4 x lOs
~ 'i.t.c.t:d-i 0 'r\.,!;
c.oeJfue'f\1s
X 0,751; u.~
8ro 'YOCI..;) 5 rW" rN'.,..k '" b r",b "b ,- b -:::. ~tJ (0 75U) Uh
~r-> ~c....;l. to 'MQ~ Lw-- k r~<.: 200 I U;....
i.e) fx..l:, = :l (0.750 t- .oo4&1I)Ul, =,
'hTn "'tOe.> 6 abfo't'VI TY'~Y" ~b
~ .!l<r-, ( ) U AI.
:tb ~ Y1)(,.> (0 t, ~~b
pk ) be.;>.m') (y l L
},r.' ;>.to (01" II) /..(! 0;:..
I ~:c 0
----------
o.
3.0.,.... J.,.r, .,.../..u 0.6"ro~
.o! <>. 6 Nt!:. -::: ~ ) lib.
'mt ~ ..,./wyPMCb 31'0 fli\ +. k h .
"/ r.. - ~ ( ,.,. <'>uo) (J~ 6 r./;
, ~tO )< I; ~t:ll)O',PI>
I ftJ\?I, := ':>C'l'1> ( D + I~. /!'Jo) ~ = Ub
f Pxb•j"""" ~ ® m Wl bt Y D-~ Vb~- ~ " -------.i F,C>1.. ~ a b
=: ~ (I:.) ''la.b ~b
'in.,.. 'to u~ @ k.~b ~ k. k.
.200 ( o} IlbFilb c
';kS'J (1.3 "t C)) Ifb = 0',~ i f~ : ~
~ ')'0 (6 ....,./:..c 1:6t r> 0.1>r-! -= :J ~ ( .,..,.. Ii 6~ ) 1ft. ~b
~& ~ "'rt1W (i) f.o~ 'MQ~L~ ~c
'f'" Y~'M (8 o.bf~~ N ",h "'6
= 200 (- I~' 7~1 ) Lt z~
r~~ ~ 'YJu... 0') jvow- 'lV\4! vJ.,c,.y- II Mk (0 ) ut:..
'f./ -='cro -;) ;,e., P",~ - ;l(ro C- I 'g' 7~ (:, +0) Itt, = )( 12' 7S ()j,
o
, a
~
r~b
~~ /)"110) (lo f'vor-. bi'..v a b r-o.! C4c r ~ -= ~ (-/'g·75) B.z , ."... Yb (.~ (il fr-o""" ........ w-bw b (
be b~F')(b -= :Km (0 )O:Z6
C. P I p~h - .:l. (- I . 7s oj- D) r;. ~6 = -;) )( 18 ' 75 tJ~.6
lOOffl kN
tJ.b 1!o· 4- 'i I 'f ?'7"I"M 1IIJi, = - o· 3cr9 ~ 'mm. :::S:. a
e o· 00 169 -rod..1b
(Note:ub and /)b
not shown)
lOOf--i2 kN
