(a)
The value of principal stress
(a)
Answer to Problem 2.85P
The value of the principal stress
Explanation of Solution
Given:
Yield strength of the material is
Principal(normal) stress in x-direction is
Principal(normal) stress in y-direction is
Principal(normal) stress in z-direction is
Concept used:
Here
Write the Maximum distortion energy theory (Von mises Theory) as,
Here,
Calculation:
Substitute
Conclusion:
Thus the value ofthe principal stress
(b)
The value of principal stress
(b)
Answer to Problem 2.85P
The value of principal stress
Explanation of Solution
Given:
Yield strength of the material is
Principal stress in x-direction is
Principal stress in y-direction is
Principal stress in z-direction is
Concept used:
Here
Write the Maximum distortion energy theory (Von mises Theory) as;
Here,
Calculation:
Substitute
Conclusion:
Thus the value ofthe principal stress
Want to see more full solutions like this?
Chapter 2 Solutions
EBK MANUFACTURING PROCESSES FOR ENGINEE
- What results do we get when shear stress is applied to homogeneous isotropic material?arrow_forwardIn the attached picture there is a sketch of a socket wrench. Assume the wrench is held at a fixed point “A”. The yield stress of the material is known to be 500 MPa. Answer the questions below Describe the stresses at point “A” and their causes and calculate the stresses. Determine the factor of safety against yield assuming the Tresca yield criteria. Determine the factor of safety against yield assuming the von Mises yield criteria using both principal stresses and “Cartesian” stresses. Do your values match or not, and is this expected? Explain. Do the calculated values make sense with the respect to the Tresca value? Explain, why or why not?arrow_forward1. A part made of Aluminum 6061-T6 has a yield strength = 400 MPa. For each stress state below, draw all 3 Mohr's circles, find the principal stresses, and calculate the safety factor against yield using both the distortion-energy (von Mises) and maximum shear stress (Tresca) criterions. (If relevant) A clearly labeled diagram (or diagrams) clearly pertaining to your analysis with a coordinate system and relevant labels. Final answer with appropriate units and significant figures. You can use the fprintf() command in MATLAB to format numerical results A 2-3 sentence reflection on your answer. Does it make sense? Why or why not? What are some implications?arrow_forward
- An element of a ductile material on the free surface of a component is subjected to the stress system shown in Figure 1. (e) If the material has a yield stress of 300 MNm-², and recognising that plane stress conditions prevail in the element (i.e., at the free surface), determine the factor of safety against yielding using; the Tresca yield criterion, and the von Mises yield criterion. (i) (ii) 100 MN m-² 200 MN m-² 80 MN m-² 100 MN m-² 2001 200 MN m-² Figure 1: Stresses on element 1.. Xarrow_forwardExample 2 Assume that a material has true stress - true strain curve given by: O = 100,000 ɛ0.5 psi. Calculate the true ultimate tensile strength and engineering UTS of this material. 96arrow_forwardb) A hollow tube of cross-section as shown in Figure 2.2 is subjected to an axial tensile force of 100kN. If the tensile yield stress of the material is 280MN/m², use the von Mises yield criterion to determine if a torque of 6kNm can be applied without causing the tube to yield. * -50 mm 45 mm Figure 2.2: Hollow tube profilearrow_forward
- During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of +140 MPa, and a minimum stress of -70 MPa. The R-ratio (minimum stress to maximum stress) for this cyclic loading is (round off to one decimal place)arrow_forwardA bar of a steel alloy that exhibits the stress–strain behavior shown in Animated Figure 7.34 is subjected to a tensile load; the specimen is 375 mm (14.8 in.) long and has a square cross section 5.5 mm (0.22 in.) on a side.(a) Compute the magnitude of the load necessary to produce an elongation of 7.5 mm (0.30 in.). _____________________________________________________ N (b) What will be the deformation after the load has been released? _______________________________________________________ mmarrow_forwardDefine the term Absolute Maximum Shear Strain?arrow_forward
- A material has the following properties, ultimate Sul = σul = 350mpa, the strain hardening exponent n=0.20. Determine the value for the strength coefficient K.arrow_forwardLet's assume that the stress-strain elongation curve of a high-strength steel is given by this equation. o = 1.4*10º"ɛ 3 2.9*10*ɛ ² + 2.1*10°z Calculate the yield limit value of this steel. Oa (kgf/cm³) (For Yield Strength, use a straight line from the starting point and Calculate wwwwwww ww w m by moving the line parallel to the given curve)arrow_forwardQuestion 3 The state of stress at a point is described by: [200 0 0 0 155 0 0 0 -150] M MPa If the point is taken from a part that is made from a material with a yield stress, Gyield = 345 MPa, check weather the failure occurs according to Tresca or von Mises criteria. Which one of this criteria is more conservative? Explain.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY