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# Quiz12 - Problem 9.5-10 A beam ABC having ﬂexural...

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Unformatted text preview: Problem 9.5-10 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"5kN-rn2 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 (3-1. Case 4: 5"; = “ 3E} CONSIDER AB As A SIMPLE BEAM W0 A B m M0 = PL: _ MGL, PLle Table 0-2. 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 0.4-3 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 SHEAR-FORCE AND BENDING-MOMENT 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 10.4-6 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 bending-moment diagrams, labeling all critical ordinates. ’ m" 'm' . 4 + :4..— L _——+_— 2L__J KAI RH RC Solution 10.4-6 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 FORCE-DISPLACEMENT 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 10.4-3 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. Comm-r113th 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 ! —D-1 — 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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Quiz12 - Problem 9.5-10 A beam ABC having ﬂexural...

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