WV. ii. Factors of safety by measurements of various points along the load lines: Point A (-200 MPa, da 100 MPa) Point B (0-150 MPa,d=-100 MPa) MSS DE Factors of safety predicted by the MSS and DE equations: Point A (=200 MPa,σ = 100 MPa) MSS DE Point B (-150 MPa,d=-100 MPa) Load at which the frame will experience initial yielding: Since the stresses vary linearly with the load, the yield load can be predicted from the factors of safety: Point A Load at the given stress state (=200 MPa, da = 100 MPa): F= 4 kN Point B Load at the given stress state (-150 MPa, da=-100 MPa): F= 4 kN MSS DE 1. A machine frame is made of steel with a yield strength of Sy = 400 MPa. When loaded in a test fixture, the stresses were found to vary linearly with load. Two points A and B on the surface of the frame were found to be most critical. With a 4-kN test load, stresses at these points were as in the sketches below: d-100 MPa --100 MPa d-200 MPa d-150 MPa Use the template on the following page to answer these questions: (i) A scaled drawing of the failure locus for steel using the Distortion Energy (DE) theory is shown on next the page. Mark the axes labels and the yield strength values on the σ-σg axes. Then, draw the failure locus for the Maximum Shear Stress (MSS) superimposed on the given - plot to scale, represent the given stress states at points A and B on the plot, and draw the load lines corresponding to the two points. (ii) From the load lines drawn in part (i), graphically estimate the factors of safety and predict which of the two points will experience initial yielding first according to (a) the MSS theory and (b) the DE theory. (ii) Using the equations for the MSS and the DE theories, compute the factors of safety for both points A and B at the 4-kN test load according to the MSS theory and the DE theory. (iv) Compute the test loads at which the frame will experience initial yielding according to the MSS theory and the DE theory. Solution to Problem #1 1. бр ii. Factors of safety by measurements of various points along the load lines: GA

WV. ii. Factors of safety by measurements of various points along the load lines: Point A (-200 MPa, da 100 MPa) Point B (0-150 MPa,d=-100 MPa) MSS DE Factors of safety predicted by the MSS and DE equations: Point A (=200 MPa,σ = 100 MPa) MSS DE Point B (-150 MPa,d=-100 MPa) Load at which the frame will experience initial yielding: Since the stresses vary linearly with the load, the yield load can be predicted from the factors of safety: Point A Load at the given stress state (=200 MPa, da = 100 MPa): F= 4 kN Point B Load at the given stress state (-150 MPa, da=-100 MPa): F= 4 kN MSS DE 1. A machine frame is made of steel with a yield strength of Sy = 400 MPa. When loaded in a test fixture, the stresses were found to vary linearly with load. Two points A and B on the surface of the frame were found to be most critical. With a 4-kN test load, stresses at these points were as in the sketches below: d-100 MPa --100 MPa d-200 MPa d-150 MPa Use the template on the following page to answer these questions: (i) A scaled drawing of the failure locus for steel using the Distortion Energy (DE) theory is shown on next the page. Mark the axes labels and the yield strength values on the σ-σg axes. Then, draw the failure locus for the Maximum Shear Stress (MSS) superimposed on the given - plot to scale, represent the given stress states at points A and B on the plot, and draw the load lines corresponding to the two points. (ii) From the load lines drawn in part (i), graphically estimate the factors of safety and predict which of the two points will experience initial yielding first according to (a) the MSS theory and (b) the DE theory. (ii) Using the equations for the MSS and the DE theories, compute the factors of safety for both points A and B at the 4-kN test load according to the MSS theory and the DE theory. (iv) Compute the test loads at which the frame will experience initial yielding according to the MSS theory and the DE theory. Solution to Problem #1 1. бр ii. Factors of safety by measurements of various points along the load lines: GA

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.4.5P: An element on the top surface of the fuel tanker in Problem 7.2-1 is in biaxial .is in the and is...

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