CE412 Advanced Structural Analysis Exam 4 Study Guide Exam Date: March 28, 2018

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1 E412 dvanced Structural nalysis Exam 4 Study Guide Exam Date: March 28, 2018 E412 dvanced Structural nalysis Exam 4 Study Guide Exam Date: Wednesday, March 28, 2018 Exam Format: 100 points Time imit: 50 minutes losed ook, losed Notes FEM Formulae Will e Given. eam formulae or deflections may be given with some problems. overage: essons 18 to 23 Given Formulae: ll Fixed End Moment Formulae will be given Steel Manual eam Formulae may be given (for Force Method Problems) esson Objectives and Sample Problems IGNORE SHER DEFORMTIONS FOR PROEMS. alculate unknown reactions for a 2-degree of indeterminacy beam due to applied loads. 1. Problem (45 points). Use the Force Method to plot the moment diagram for the beam below. Given: the three-span continuous beam with overhangs below, with distributed load. EI = constant 7 ft. 15 ft. 15 ft. 15 ft. 7 ft. SO GIVEN: Deformed shape and analysis results, below (units: kips, feet) 40894/EI 1313/EI 2. Problem (50 points). Use the Force Method to plot the moment diagram for the beam below. Given: the beam below, with distributed load. EI = constant 15 ft. 15 ft. 15 ft. SO GIVEN: Deformed shape and analysis results, below (units: kips, feet) 90703/EI /EI /EI 2813/EI D 1125/EI 4500/EI 3. Problem (45 points). Use the Force Method to determine reactions and plot the moment diagram. eam D is continuous. Member E and F are pin-ended. DO NOT ignore axial deformations. HINT: The easiest way

2 E412 dvanced Structural nalysis Exam 4 Study Guide Exam Date: March 28, 2018 to think about this problem is to consider the axial members to be springs and adjust the compatibility statement, accordingly. Given: D has EI = 1,000,000 kip-in 2, E and F have E = 1000 kips. F E 100 inches 50 inches 0./inch 100 inches 100 inches 100 inches SO GIVEN: Deformed shape and analysis results, below (units: kips, feet) 0./inch Problem (20 points). Determine the reactions and moment diagram for the previous eam D IF the axial members E ND F are, instead, INFINITEY STIFF. Derive the slope-deflection equations for a member without support translation. 5. Problem (20 points). Use the onjugate eam Method to show that M = (4EI/) EI = onstant M = (4EI/) ompute beam end-moments, given end-slopes. 6. Problem (30 points). oncentrated moments are applied to and, causing equal clockwise rotations of and, = = rad. Plot the moment diagram for the frame (on the compression side), then determine the magnitudes of concentrated moments that are applied to and. Hint: do this qualitatively, at first, as it will prevent subsequent blunders. Given: EI = 100,000 kip-ft 2 for all members. E F

3 E412 dvanced Structural nalysis Exam 4 Study Guide Exam Date: March 28, Problem (35 points). There are no direct forces applied to the frame, but fixed support has rotated clockwise by rad. Plot the moment diagram for the frame (on the compression side). Hint: do this qualitatively, at first, as it will prevent subsequent blunders. Given: EI = 100,000 kip-ft 2 for all members. ompute the end-slopes and end-moments at joints in an indeterminate beam, loaded with concentrated moments at joints (with other objectives) Describe the meaning of the fixed-end-moment (FEM) 8. (10 points). oth eam (1) and eam (2) are intended to have fixed supports at and. However, Support for eam (2) has rotated clockwise, slightly. Knowing this, circle the correct answer. eam (2) eam (1) w w EI = onstant EI = onstant Relative to eam (1): a. eam (2) will have greater moment magnitude at. b. eam (2) will have lesser moment magnitude at. c. eam (2) will have greater moment magnitude at and at. d. eam (2) will have lesser moment magnitude at and at. e. eam (2) will have greater moment magnitude at and lesser moment magnitude at. f. eam (2) will have lesser moment magnitude at and greater moment magnitude at. 9. ircle the correct answer (5 points). For the 2-Span beam with an applied concentrated moment of 10 kip-ft at joint, as shown, with constant EI: M = 10 kip-ft a. FEM = 10 kip-ft b. FEM = -10 kip-ft c. FEM = 5 kip-ft d. FEM = 0 kip-ft ompute the end-slopes and end-moments at joints in an indeterminate beam without support translation, loaded anywhere along the span using the general Slope-Deflection Equations. ompute the end-slopes and end-moments at joints in an indeterminate beam without support translation, loaded anywhere along the span using the Pin-Supported End-Span Shortcut. 10. Problem (35 points). Use the slope-deflection method to solve for the internal moment at point. Given: EI = constant

4 E412 dvanced Structural nalysis Exam 4 Study Guide Exam Date: March 28, kips 12 kips 8 ft. 8 ft. 8 ft. 24 ft. 11. Problem (40 points). Use the slope-deflection method to plot the moment diagram for the two-span continuous beam below, with 10-kip point loads at the center of each span. EI = constant 10 kips 10 kips 15 ft. 25 ft. 12. Problem (10 points). Use the slope-deflection equations to determine the slope at point. Given: EI=10,000,000 kip-in 2 0.s/inch Solve unknown slopes (and moments) in frames when sidesway is prevented. 14. Problem (35 points). Use the slope-deflection method to draw the moment diagram for. onnection is rigid. Foundation is fixed. Foundation is a pin. EI is constant for all members. Ignore axial deformation. 1kip/ft 5 8 kips Problem (30 points). Use the slope-deflection method to solve the necessary end-moments for the rigid frame and plot the moment diagram. EI is constant. Supports and D are pins; is a fixed foundation. Ignore axial deformation. 2 kip/ft D 32

5 E412 dvanced Structural nalysis Exam 4 Study Guide Exam Date: March 28, Problem (30 points). Use the Slope-Deflection Method to compute end-moments and draw the moment diagram for. onnection is rigid. Foundations and are fixed. EI is constant for all members. Ignore axial deformation. 5 kips 10 kips