CVEEN3510_Homework3-Solutions

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University of Utah *

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3510

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Civil Engineering

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Apr 3, 2024

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Page 1 of 6 CVEEN 3510-001 Civil Engineering Materials Homework 3 – Grading Scheme Note: Only key points are mentioned in the grading scheme. Your answers must be in full sentences. 1) Textbook Problem 4.3 (10 points) An aluminum alloy specimen with a radius of 0.28 in. was subjected to tension until fracture and produced results shown in Table P4.3. (Refer the textbook). a) Using a spreadsheet program, plot the stress – strain relationship. (2 points) b) Calculate the modulus of elasticity of the aluminum alloy. (1 point) c) Determine the proportional limit. (1 point) d) What is the maximum load if the stress in the bar is not to exceed the proportional limit? (2 points) e) Determine the 0.2% offset yield strength. (1 point) f) Determine the tensile strength. (1 point) g) Determine the percent of elongation at failure. (2 points)
Page 2 of 6 2) List five factors that make aluminum an attractive structural engineering material. (5 points) • Use of exposed surface as the finish. • Minimizing weight. • Easy recyclability. • If we use bolted connectors, it facilitates dismantling and reassembling for a new project. • High strength to weight ratio. 3) Why does the iron – carbon phase diagram go only to 6.7% carbon? What is the typical maximum percent of carbon in steel used for structures? (5 points) - matter of convention. - Each carbon atom bonds with three iron atoms to form iron carbide (cementite). - Iron carbide is 6.7% carbon by weight. Thus, on the phase diagram, a carbon weight of 6.7% corresponds to 100% iron carbide. 4) Why is reinforcing steel used in concrete? Discuss the typical properties of reinforcing steel. (5 points) - Concrete is brittle and has negligible tensile strength. - Reinforcing steel carries the tension when structural concrete members are subjected to tensile and flexural stresses. 5) The following laboratory tests are performed on steel specimens: a. Tension test b. Charpy V notch test c. Bend test What are the significance and use of these tests? (5 points)
Page 3 of 6 Tension test: The tension test (ASTM E8) is performed to determine the yield strength, yield point, ultimate (tensile) strength, elongation, and reduction of area. It is used in design of steel structures. (1 point) The Charpy V Notch impact test (ASTM E23) is used to measure the toughness of the material or the energy required to fracture a V-notched simply supported specimen. The test is used for structural steels in tension members. (2 points) Bend test (ASTM E290) evaluates the ability of steel, or a weld, to resist cracking during bending. Reinforcing steel has to be bent to different shapes for use in reinforced concrete structures. The ductility to accommodate bending is checked by performing this test. (2 points) 6) Textbook Problem 3.34 (10 points) A grade 36 round steel bar with a diameter of 0.5 in. and a gauge length of 2 in. was subjected to tension to rupture following ASTM E-8 test procedure. The load and deformation data were as shown in Table P3.34 (Refer the textbook). Using a spreadsheet program obtain the following: a) A plot of the stress – strain relationship. Label the axes and show units. (1 points) b) A plot of the linear portion of the stress – strain relationship. Determine modulus of elasticity using the best fit approach. (1 points) c) Proportional limit. (1 points) d) Yield stress. (1 points) e) Ultimate strength. (1 points) f) When the applied load was 4.07 kips, the diameter was measured as 0.499905 in. Determine Poisson’s ratio. (2 points)
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Page 4 of 6 g) After the rod was broken, the two parts were put together and the diameter at the neck was measured as 0.416012 in. What is the true stress value at fracture? Is the true stress at fracture larger or smaller than the engineering stress at fracture? Why? (2 points) h) Do you expect the true strain at fracture to be larger or smaller than the engineering strain at fracture? Why? (1 points) f) Poisson ’ s Ratio = – Lateral strain / Longitudinal strain Lateral strain = change in diameter / diameter = (0.5 - 0.499905) / 0.5 = -0.00019 in./in. at P = 4.07 kips, the displacement = 0.00141 in (from Load vs Displacement data in the table) Longitudinal strain = change in length / length = 0.00141 / 2 = 0.000705 in./in.
Page 5 of 6 Poisson ’s Ratio = – Lateral strain / Longitudinal strain = 0.00019 / 0.000705 = 0.27 g) Cross sectional ares at failure = π (0.416012) 2 / 4 = 0.136 in 2 True stress = 7.87 / 0.136 = 57.868 ksi The true stress at failure (57.868 ksi) is larger than the engineering stress (40.078 ksi) since the cross- sectional area at the neck is smaller than the original cross-section. h) The true strain at failure is larger than the engineering strain at failure since the increase in length at the vicinity of the neck is much larger than the increase in length outside of the neck. 7) A Charpy V Notch test was conducted for a steel specimen. The average values of the test results at four different test temperatures were found to be 15 J at -45°C 21 J at -18°C 60 J at 5°C 75 J at 40°C A bridge will be located in a region where specifications require a minimum of 35 J fracture toughness at 0°C for welded fracture-critical members. If the bridge contains a welded flange in a fracture-critical member, does the steel have adequate Charpy V notch fracture toughness to be used for this bridge? Show your supporting calculations. (5 points) From the graph, the energy corresponding to 0 o C is about 54 N.m. Therefore, the steel member has adequate Chary V-notch fracture toughness.
Page 6 of 6 8) The World Trade Center collapse on September 11, 2001, was due in large part to steel failure. Using the Internet, investigate what happened to the steel in this structure and relate it to fundamental steel properties. (5 points) Make your own conclusions from the information that you gather. Some references: https://news.asu.edu/20210908-solutions-engineering-students-still-learning-collapse-world-trade- center . Banovic, S. W., Foecke, T., Luecke, W. E., McColskey, J. D., McCowan, C. N., Siewert, T. A., & Gayle, F. W. (2007). The role of metallurgy in the NIST investigation of the World Trade Center towers collapse. JOM, 59, 22-30.
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