CIVE 410 Homework 4 with Solution, Spring 2011

American University of Beirut Civil Engineering Dept. Faculty of Eng. & Arch. Structures Il — CIVE410 - Homework [4] Spring 2011 Problem [1] For the truss shown in the accompanying figure, assume the members have a constant EA and that all members are pin connected at their ends. Use E4=120,000 EN. [a] Determine the force in each member of the truss. Use the reaction at B and the force in member BD as redundants. [b] Determine the horizontal displacement of point D. Problem [2] The beam ABC shown in the accompanying figure has a fixed support at A and roller supports at B and C. Assume E= 200 GPa and 1=90(10°) mm’. [a] Using the Flexibility Method (Virtual Work Concept) for analysis of indeterminate structure draw the Bending Moment Diagram of the beam. Use Yp and Yc as redundants. [b] Determine the slope at B. {c] If support B has settled 1.5 cm vertically downwards, determine the supports reactions due to the given loads in addition to the vertical settlement at B. 45 kN/im Problem [3] The frame ABDF shown in the accompanying figure is fixed at A and pinned at F. Using the Flexibility Method (Virtual Work Concept) for analysis of indeterminate structure and using reactions at F as redundant determine the bending moment diagram of the frame. Neglect axial and shear deformation. Use EJ= 2.133x10° kKN.m?. | Fixed Support atA | Problem [4] The queen-post trussed beam is used to support a uniform load of 4 k/ft. Determine the force developed in each of the five struts. Neglect the thickness of the beam and assume the truss members are pin connected to the beam. Also, neglect the effect of axial and shear deformation in the beam ABDF. The cross-sectional area of each strut is 3 in? and for the beam I = 600 in’. Use E= 29,000 ksi. 4 kift 1 o 2 G [+ ye] 06 | ~Gvz - 34 1S . 21822. 4.22 BYE |é fip| lo| |-isvz o o| (382 4.963 Bolt 12 |-"h| @ | ~{BV% ° a| 45| o $. F038 231" 5 a {| oO ° oO 5 ° L4297 g 3 i, o o| [-3%2[ 1.5 3 - 2,059 | #| (sur j-evz| 4 [- {36 a 3 a] | 3h 981 HOF el [gzlo ld ioe lo o oO 3iv2. la 6.077 ae Sit 48! FO Ht a let Ahel_t 7 ef appt B | sph tndichbes | y, | + =| — + AG awe fies pa} sathe| lzezecmn pes ra : (W3/TJN,.TN)wing = q 12 juawareidsiq (1) waqosd - [p]/MH -OTP3AID BLEZ'7=CX ZNZX+TNTX+ON =JN $9Z0°9=TX ZEOL'0L Q9@v4'S | ES8V'VT | O28T'9- | OOOO'ST | SET PZ gaago0'a | 00000 $9£0°9 0aa0°0 9vz'V 00000 00a0'0 a000°0 Lofefelexe} lelelelon 0000'0 9227 8 €€46'TT | TLOZ‘O- 7T66'E- ET2T'Z 92vz'p | QQ00'E- | LGG7'S2 | 9666'SE- | TLZOZ‘O- | OOOO'T | ES8H'e- | Ivey Gj 0000°0 0000°0 Q6S0'Z- o000°€ gooos’t | etztz- | 0000°0 feleleleye} oooo'tT | T404°0- | O000°0 lelelelees 9 0000°0 0000°0 8967't- lefelelexe} Qods'T 0000°0 0000°0 0000°0 00000 | TZ40Z'0- | 0000°0 ielelelok S L6QT'EZ | OOOO'T 7EOL'L 0000°0 ooos'T 0000°0 0000'0 | O9St'Sz- | QQ00'O | TZOZ'0- | O000°ZT | O000'E v 80202 | T4020 6206'9 ETZT'S 0000"0 goao0'o | ZsSv'sz- | Q000°0 | T404°0- {| 0000°0 ES8t'S 92be'7 € EEC T 000s‘0 T2787 00s2°0 goos'T | ZO90'T- | O000°6 | O8ZZ'2T- | OOOS'O ; TZ04Z'°0- | O000°9 0000"e @ v8Z9°0T | O00S°0 68TTL aosz'0 a000"0 00000 0000°6 0000°0 000s'0 0000°0 0000'9 (olelelens T TIN. TN i1TN JN TENZN TINTN ON 1 Jaqual! if L a kent) B Pr a nae Bhkge J a: =) iG hot metre Flastit an _@ E 25) 2 _[ | ateeaal phat fh i int > Ez) | tla T th Heng er & Bopxuok 402! Wore 1a lool L a | wae | | Ane 7913931 &. = £3, 383) = Z as I I peat te eee J Pe A fot | 45™ tho, L Sake S| a = T L p RAT Sp dicen | Rais! | USE FOR AN WER on ' - = Pa d USE FOR | | 1A it == 2 4 la ¢ Hor mites ett laduoke), beac | 7 TE a Pagaice | “LZ Ed - tie BEI PEP PP ea ap 2hS po —_ 38 1: ‘2. 3,33 i” Et EZ. a [4 4 ia bi Z l} yA 40a a M4 26.07