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Landis S2010 Exam 1

# Landis S2010 Exam 1 - ASE 321 — Structural Analysis TEST...

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Unformatted text preview: ASE 321 — Structural Analysis TEST 1 Spring 2010 - Landis Name EID Instructions: Show all of your work. Place a box around your ﬁnal answers and include units if necessary. While correct ﬁnal answers are of course important, setting up the correct equations to be solved without the final solutions will be awarded signiﬁcant partial credit if the solution procedure is explained properly. The structure above consists of a horizontal beam element (E, A, I, L) built in to a wall on its left side and supported by a roller on the right, and two truss elements (E, A) connected to the beam and to each other with pins. The angle between each of the trusses and the beam is 45°. At the center node both the vertical and horizontal displacements are speciﬁed. The truss to the right has an axial load speciﬁed along it, x/Ex’ L . truss element from the center node towards the right node. Note that 33’ is the local coordinate measuring the distance along the p(:v’) = :00 Problem 1. Consider a two-noded truss element in its local coordinate system, i.e. consider only the axial displacements of the two nodes. Determine the shape functions for such an element. For the element shown in the structure above, determine the consistent nodal loads for the speciﬁed continuous loading. (25 points) Problem 2. Describe the types of degrees of freedom that exist at each of the nodes shown in the structure. Do not consider any constraints at this point. Determine the full structural stiffness matrix for the structure. (25 points) Problem 3. Using 11.0 = 0 and no :2: 0 determine all of the unknown degrees of freedom in the structure. Hint: be sure to rotate the consistent nodal forces into the global coordinate system. (25 points) Problem 4. Determine all of the reactions at the built-in support. (25 points) ASE 321 - Structural Anal sis TEST 1 S rin 2010 - Landis EA EA —-— 0 0 —— 0 0 L L 12E] 6E] 12E] 6E1 L3 7 _ L3 ? 6E] 4E1 0 6E] 2E] 2 _ L2 L L2 L __>1 [K beam ] — I EA EA 3 —— 0 — 0 0 L L 12E] 6E1 12E] 6E1 0 _ L3 "L7 L3 __LT 6E1 2E1 6E1 4E1 0 T — - 2 “— L L L L CC CS —66 ‘CS K _ EA cs ss —cs —ss [ truSs] _ T —CC —CS CC CS —CS‘ —SS CS SS c=cos0, s=sin0 “#4 (lex') = CL, + a‘x' Ul=u(°)=ao j Q0=Ul UL: “(l-l) = Q0? Q'LI 6H .. {XL-bl, L’ I l I ~u / Y X => WX>= w +01, 9x = 0- 3M. +<FML %) W N! NZ. QWE {Luncﬁmﬁ NOGQRP Qua!" (in xeocd CEOF‘CUAkUZ Xi)! L L I / ~ 5* a ’= Pﬁjx’ L5. 4’ = M9— xz J}. L V15}: 9-9 = W?— L'L _ Vii (Elf =£3E =L(23> T<Z‘)‘L<~—:) g; L/ / J'“ t J‘“ ’5 L/ HEX / 'FDL /)(I /“ F132 X F2= JP T: M“ YJWUW ‘ T: gﬂL 05 L’" 0J1 LE. . Jug): r... (qu33: L— 13 3J1 Chevron www.chevron.com a www.chevron.com £0 ton 31334) \,2)+,§) 4,8 : d/F;f«Q.6\bQW\C.~I’§ 3)€ ‘ Y‘o havh‘ an, O -6 Eli} Ara/l. l ~I *l I 4 ”t g I l 6“ . Chevron www.chevron.com ' www.chevron.com ...
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Landis S2010 Exam 1 - ASE 321 — Structural Analysis TEST...

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