CIVE 411 Final Two Previouses, Fall 2016

AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 411 - Fall Semester, 2015 Instructor: Mayssa Dabaghi 1 Final Exam Saturday 12 December 2015 Closed Books - Duration: 120 min Name: ID#: NOTES o 4 Problems- percentage of each question as indicated o Start each problem on a new page o Write down the equations you use to get partial credit o Write neatly and be organized o Useful Tables provided (Appendix) o There is a ZERO-TOLERANCE policy on cheating. Problem 1: _ _ _ / 10 Problem 2: _ _ _ / 45 Problem 3: _ _ _ / 40 Problem 4: _ _ _ / 10 GRADE: _ _ _ / 105 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 411 - Fall Semester, 2015 Instructor: Mayssa Dabaghi 2 Problem 1: (10 points) The frame shown in Figure 1 is fixed at its base. Using qualitative influence lines, determine the arrangement of a uniformly distributed live load �� to cause the maximum positive bending moment at A. Figure 1 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 411 - Fall Semester, 2015 Instructor: Mayssa Dabaghi 3 Problem 2: (45 points) The plan view of a grid of floor beams, resting on pillars at A, B, C, and D is shown in Figure 2.a. The loading consists of 2 concentrated forces � (gravity loads) at mid-span of AE and EB, as shown. Beam AB has flexural rigidity �� and zero torsional rigidity. Provide your answers to the following questions in terms of �, ��, ��, and ��, whichever applicable. Axial and shear deformations are neglected. Figure 2.a Part I: First, it is assumed that beam CD is infinitely stiff, such that beam AB can be idealized as follows: Figure 2.b [A] Using the Force Method of analysis, and using �� as redundant, draw the shear and bending moment diagrams of beam AB. (20 points) □ [B] Using the principle of virtual work, and making use of symmetry, compute the deflection Δ at mid-span of AE and EB (i.e., at the location of the applied forces). (10 points) □ AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 411 - Fall Semester, 2015 Instructor: Mayssa Dabaghi 4 Part II: Now, it is assumed that beam CD also has stiffness ��, such that beam CD can be idealized as an axial spring, and beam AB can be idealized as follows: Figure 2.c [C] If CD is simply supported at C and D, what is the value of ��? (5 points) □ [D] Compute ��. Compare with �� in part [A] and comment. (10 points) □ AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 411 - Fall Semester, 2015 Instructor: Mayssa Dabaghi 5 Problem 3: (40 points) Frame ABC is loaded as shown in Figure 3. The frame is fixed at A and supported by a roller at C. Notice: The flexural rigidity is (EI) for the beam and (2EI) for the column. The lengths are also different! Using the slope-deflection method, [A] Compute �� (horizontal displacement at B) and �� (rotation at B). (20 points) □ [B] Draw the shear and moment diagrams of the frame. (15 points) □ [C] Use your results in [A] and [B] to sketch the deflected shape. (5 points) □ Neglect the effect of axial and shear deformations. You can use � = � � and �� = ��, ��� ��. ��. Figure 3 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 411 - Fall Semester, 2015 Instructor: Mayssa Dabaghi 6 Problem 4: (10 points) Beam AB shown in Figure 4 is a propped cantilever; it is fixed at A and supported by a hinge at B. �� is constant. The slope-deflection equation for a propped cantilever span AB is given by: ��� = 3�� ��� �� − 3�� ��� ��� + ����� � Prove the first term of this equation, i.e., that the fixed-end moment at A due to node rotation �� is given by ��� = ��� ��� ��. Figure 4 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 411 - Fall Semester, 2015 Instructor: Mayssa Dabaghi 7 APPENDIX – Useful Tables AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 411 - Fall Semester, 2015 Instructor: Mayssa Dabaghi 8 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 410A - Spring Semester, 2015 Instructor: Mayssa Dabaghi 1 Final Exam Saturday, 9 May 2015 Closed Books - Duration: 120 min Name: ID#: NOTES o 5 Problems- percentage of each question as indicated o Useful Tables provided (Appendix) o Provide all answers on these question sheets o Write neatly and be organized o There is a ZERO-TOLERANCE policy on cheating. COMMENTS --------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------- Problem 1: _ _ _ / 10 Problem 2: _ _ _ / 15 Problem 3: _ _ _ / 35 Problem 4: _ _ _ / 15 Problem 5: _ _ _ / 30 GRADE: _ _ _ / 105 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 410A - Spring Semester, 2015 Instructor: Mayssa Dabaghi 2 Problem 1: (10 points) The frame shown in Figure 1 is fixed at its base. On which beams (or portions thereof) should distributed loading be placed to maximize the positive moment at A. Figure 1 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 410A - Spring Semester, 2015 Instructor: Mayssa Dabaghi 3 Problem 2: (15 points) Assemble the flexibility matrix of the truss structure shown in Figure 2. �� is constant. Use �� and �� as redundants. Do NOT solve for the redundants. Figure 2 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 410A - Spring Semester, 2015 Instructor: Mayssa Dabaghi 4 Problem 3: (35 points) Frame ABCD is loaded as shown in Figure 3. The frame is fixed at B and C, and supported by a roller at A. Notice: The flexural rigidity is (EI) for the beam and (2EI) for the columns. The lengths are also different! Using the slope-deflection method, [A] Compute �� (horizontal displacement at A) and �� (rotation at D) (15 points) □ [B] Draw the moment diagram of beam AD (10 points) □ [C] (*) Use the principal of virtual work to compute the vertical displacement at the mid-span of AD. (Hint: carefully select your virtual structure) (10 points) □ Neglect the effect of axial and shear deformations. You can use � = � � and �� = ��, ��� ��. ��. Figure 3 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 410A - Spring Semester, 2015 Instructor: Mayssa Dabaghi 5 Problem 4: (15 points) Beam ABC shown in Figure 4 is fixed at A and C. Assemble its classical stiffness matrix. �� is constant. Do NOT solve for the unknown DOFs. Neglect the effect of axial and shear deformations. Figure 4 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 410A - Spring Semester, 2015 Instructor: Mayssa Dabaghi 6 Problem 5: (30 points) Frame ABCD is loaded as shown in Figure 5. It is fixed at A, B, and C. �� is constant. [A] Select a method of analysis for this structure. Justify your choice. (2 points) □ [B] Draw the shear and moment diagrams of the frame. Comment on how the applied moment is distributed. (13 points) □ [C] Sketch the deflected shape. (5 points) □ Now in addition to the concentrated moment, the support at B settles by Δ� = 1 cm downwards. [D] Draw the moment diagram and sketch the deflected shape. (10 points) □ Neglect the effect of axial and shear deformations. You can use � = ��� ��. �, � = � �, and �� = ��, ��� ��. ��. Figure 5 AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 410A - Spring Semester, 2015 Instructor: Mayssa Dabaghi 7 APPENDIX – Useful Tables AMERICAN UNIVERISTY OF BEIRUT Department of Civil & Environmental Engineering CIVE 410A - Spring Semester, 2015 Instructor: Mayssa Dabaghi 8