The stress–strain relationship shown in Figure P1.16 was obtained during the tensile test of an aluminum alloy specimen.
Determine the following:
a. Young’s modulus within the linear portion
b. Tangent modulus at a stress of 45,000 psi
c. Yield stress using an offset of 0.002 strain
d. If the yield stress in part c is considered failure stress, what is the maximum working stress to be applied to this material if a factor of safety of 1.5 is used?
Learn your wayIncludes step-by-step video
Chapter 1 Solutions
Materials for Civil and Construction Engineers (4th Edition)
Additional Engineering Textbook Solutions
Foundation Design: Principles and Practices (3rd Edition)
Java How to Program, Early Objects (11th Edition) (Deitel: How to Program)
Modern Database Management
Starting Out with C++: Early Objects (9th Edition)
Introduction To Programming Using Visual Basic (11th Edition)
Software Engineering (10th Edition)
- The data in Table 1.5.3 were obtained from a tensile test of a metal specimen with a rectangular cross section of 0.2011in.2 in area and a gage length (the length over which the elongation is measured) of 2.000 inches. The specimen was not loaded to failure. a. Generate a table of stress and strain values. b. Plot these values and draw a best-fit line to obtain a stress-strain curve. c. Determine the modulus of elasticity from the slope of the linear portion of the curve. d. Estimate the value of the proportional limit. e. Use the 0.2 offset method to determine the yield stress.arrow_forwardCompare the engineering and true secant elastic moduli for the natural rubber in Example Problem 6.2 at an engineering strain of 6.0. Assume that the deformation is all elastic.arrow_forwardA tensile test was performed on a metal specimen having a circular cross section with a diameter of 1 2 inch. The gage length (the length over which the elongation is measured) is 2 inches. For a load 13.5 kips, the elongation was 4.6610 3 inches. If the load is assumed to be within the linear elastic rang: of the material, determine the modulus of elasticity.arrow_forward
- Based in the table 1.1) Develop a best-fit equation for the relationship between stress and strain. Employ Naïve–Gauss elimination method whenever necessary.S=______+______e + _______e2 2) Determine the coefficient of determination for the equation. R2 =_______ 3) Calculate the stress value to the most accurate value at strain value 0.53.s = _______Pa4) The yield point is the point on a stress–strain curve that indicates the limit of elastic behaviour and the beginning of plastic behavior. In this case, the yield point occurs at a stress value of 80. Determine the corresponding strain value at the yield point. In any relevant method, use a stopping criterion of 0.05% e =_______ 5) The ultimate strength is the maximum point on the stress–strain curve. This corresponds to the maximum stress that can be sustained by a structure in tension. Compute the ultimate strength point of the polymeric material (strain value that gives maximum stress). In any relevant method, use a stopping…arrow_forwardThe stress–strain relationship shown in Figure was obtained during the tensile test of an aluminum alloy specimen. Determine the following:a. Young’s modulus within the linear portionb. Tangent modulus at a stress of 45,000 psic. Yield stress using an offset of 0.002 straind. If the yield stress in part c is considered failure stress, what is the maximum working stress to be applied to this material if a factor of safety of 1.5 is used?arrow_forwardA steel block has a length of 80 mm, width of 60 mm and thickness of 40 mm. The block is subjected to a uniform hydrostatic pressure of 180 kPa on all its faces. Modulus of elasticity E=200 GPa, Poisson’s ratio ?= 0.29. a.) Determine the bulk modulus of steel, b.) Determine the dilatation (e) of the material if e is the negative of the ratio of load to bulk modulus., and c.) Determine the change in volume of the steel block.arrow_forward
- The strain rosette shown in the figure was used to obtain the following normal strain data on a piece of aluminum. The plate has a modulus of elasticity of 10,000 ksi and a Poisson’s Ratio of 0.35. The strain readings were εa = 600 με, εb = 900 με, and εc = 120 με. Note: 1 με = 1 X 10-6 in/in. a) Calculate the normal strain in the x- and y- directions (εx and εy) and the shear strain (γxy) using a system of equations. b) Calculate the normal stress σx in ksi. Clearly indicate Tension (T) or Compression (C). Note: even though the normal stress in the z-direction is zero, but the normal strain in the z-direction is NOT zero. [Ans. to Check σx = 7.18 ksi (T)] c) Calculate the normal stress σy in ksi. Clearly indicate Tension (T) or Compression (C). d) Calculate the shear stress τxy in ksi.arrow_forwardA rectangular block of aluminum 30 mm * 60 mm * 90 mm is placed in a pressure chamber and subjected to a pressure of 100 MPa. If the modulus of elasticity is 70 GPa and Poisson’s ratio is 0.333, what will be the decrease in the longest side of the block, assuming that the material remains within the linear elastic region? What will be the decrease in the volume of the block?arrow_forwardIn a tensile test for an aluminum alloy, the sample used is 2 inches long and 0.5 inches in diameter. The proportional portion of the tension stress-strain diagram for an aluminum alloy is shown below. Determine the modulus of elasticity for this material: ____x106 lb/in2. Pay attention to units and calculate your answer to 1 decimal place for the unit specified above.arrow_forward
- The data shown in the table were obtained from a tensile test of a metal specimen with a rectangular cross-section of 0.2 in.? in area and a gage length (the length over which the elongation is measured) of 2.000 inches. a. Generate a table of stress and strain values. b. Plot these values and draw a best-fit line to obtain a stress-strain curve. c. Determine the modulus of elasticity from the slope of the linear portion of the curve. d. Estimate the value of the proportional limit. e. Use the 0.2% offset method to determine the yield stress.arrow_forwardA cylindrical specimen of aluminum alloy having a diameter of 12.8 mm and a gauge length (lo) of 50.800 mm is pulled in tension. Use the load–elongation characteristics shown in the following table and answer the following questions. (10p) i- Convert the data as engineering stress (σ) versus engineering strain (ε). ii- Compute the modulus of elasticity (E) (with a precision of ±5000 MPa) iii- Determine the yield strength at a strain offset of 0.002 (σy) (with a precision of ±20 MPa) iv- Determine the tensile strength (TS) of this alloy.arrow_forwardA bar of length 2.0m is made of a structural steel having the stress-strain diagram shown in the figure. The yield stress of the steel is 250 MPa and the slope of the initial linear part of the stress-strain curve (modulus of elasticity) is 200GPa. The bar is loadded axially until it elongates 6.5mm, and then the load is removed. How does the final length of the bar compare with its original length? (Hint: Use the concepts illustrated in figure below)arrow_forward
- Steel Design (Activate Learning with these NEW ti...Civil EngineeringISBN:9781337094740Author:Segui, William T.Publisher:Cengage LearningMaterials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning