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Unformatted text preview: Problem 9.510 A beam ABC having ﬂexural rigidity E! = 75 kN'm2
is loaded by a force P = 800 N at and C and tied down at end A by a
wire having axial rigidity EA = 900 kN {see figure}. What is the deﬂection at point C when the load P is applied? Ell=7"5kNrn2 P = 800 N
EA = 900 kN
H=0.5m Ll =0.5m
L2 = 0.75 m
CONSIDER BC AS A CANTILEVER BEAM
1P
'3 C‘l'
b;
PLi
Table (31. Case 4: 5"; = “
3E} CONSIDER AB As A SIMPLE BEAM W0
A B m
M0 = PL:
_ MGL, PLle Table 02. Case 7: 9;, _ 35! = 3E1 CONSIDER THE STRETCHING 0F WIRE AD 5; = (Force in AD) 2 %) DEFLECTION BC 0F POINT C L,
5c = a; + 9;, (L2) + a; 1 P3 I’LL) PEH
____E2_+12+L2 _ 4—
3E! 31:: EAL? SUB S'ITTUTE NUMERICAL VALUES: 8C 2 1.50m +1.00mm + 1.00 mm = * PLEH
EAL, 3.50 mm ‘— 544 CHAPTER 10 Stalin"! Indeterminate Beams Solution 1 0.43 Beam with an overhang Select MA as redundant. OTHER REACTIONS {FROM EQUILIBRIUM)
3P0 P
EQUILIBRIUM R, — ——2L .lita — i (2.1. + 3a) 4— l 1
RA =—{MA + Pa) R3 =—(MA +PL +Pa)
L L SHEARFORCE AND BENDINGMOMENT DIAGRAMS RELEASED STRUCTURE AND FORCE~DISPL E05. (943i Comm];le 6dill = (3“)I — (9‘): = 0
Substitute for [6A]I and (GAL. and solve for MA: _E
_1 ‘— MA 4— 645 CHAPTER 10 Staﬂcally Indeterminate Bms Problem 10.46 A continuous beam ABC with two unequal spans, one ____ I__ _ I ___q_ H
of length L and one of length 21.. supports a uniform load of intensity I;  i E ' ' ‘ l '5
(See Flam) A
Determine the reactions R A, R a. and R C for this beam. Also‘ draw the A it B _A
shear—force and bendingmoment diagrams, labeling all critical ordinates. ’ m" 'm'
. 4 +
:4..— L _——+_— 2L__J
KAI RH RC
Solution 10.46 Continuous beam with two spans
Select R B as redundant. COMPA'I'IEILITY
68 = {53% _ {63)2 = 0
EQUILIBRIUM
11 L4 4R L3 33 L
3qL 2 3qL l q — 9 =0 RB=—q— «—
RA =“r—ER3 Rc=T—§R5 12E] 9E! 16 OTHER REACTIONS {FROM EQUILIBRIUM)
RELEA SED STRUCTURE AND FORCEDISPLACEMENT RELATIONS qL l3qL
R =— R =— ‘—
" 8 C 16
A ’ ' ‘ ' ‘ ‘ " ' i' :’ C SHEAR—FORCE AND BENDINGMOMENT DIAGRAMS
A B can
eLﬁ—u—I
lquL'l
{5' =
"’1 :25; 4RBL3
9 £1 (as): = 648 CHAPTER 1] Statically Indeterminate Beams Problem 10.43 The beam ABC shown in the ﬁgure has ﬂexural rigidity 6 mm E1 = 4.0 MN‘mz. When the loads are applied to the beam, the support at " " l 3 m B settles vertically downward through a distance of 6.0 mm. ‘ = 3 '
Calculate the reaction R B at support 8. Solution 10.4—3 Overhanging beam with support settlement Select RB as redundant. Commr113th 8i,i = (53)l + (319}2 _ (38}: = A
A = settlement of support 8 Substitute for (53)" (53):, and {53)3 and solve for RR;
R — 351 L+2816P “ 61~’l’~l£ﬁlA 4—
RELEASED STRUCTURE AND FORCEvDISPL EQS. B _ 2043 9 L3
4?
i . . B C 11? L4 NUMERICAL VALUES
I ! —D1 —
A “5311 — #2048187" q = 6.0 kam P = 3.0 kN A = 6.0 mm
31. L L “ : : . 2 P
SUBSTITUTE INTO THE EQUATION FOR R B A {##3## may Ra=lllkN 4—
‘35)! — 24E! C R L3
_ B
[A i. ‘53)! _ 351
.‘. ...
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 Fall '08
 KennethM.Liechti

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