Concept explainers
Calculate the two values of
Answer to Problem 76P
The values of
Explanation of Solution
Given information:
The components of stress
The maximum shear stress
Calculation:
Consider
Modify Equation (1) as shown below.
Calculate the average normal stress
Substitute
Calculate the value u as shown below.
Substitute
Case 1:
For
Calculate the value of
Substitute
Calculate the average normal stress
Substitute
Calculate the principal stresses
Substitute
Calculate the maximum shearing stress as shown below.
Substitute
For
Calculate the value of
Substitute
Calculate the average normal stress
Substitute
Calculate the principal stresses
Substitute
Hence, the principal stresses
Calculate the maximum shearing stress as shown below.
Substitute
Hence, the value of
Case 2:
Assume the maximum principal stress
Calculate the minimum principal stress as shown below.
Substitute
The minimum principal stress
Substitute
Substitute
Calculate the value of
Substitute
Calculate the value of R as shown below.
Substitute
Calculate the principal stress
Substitute
Hence, the principal stresses
Therefore, the value of
Want to see more full solutions like this?
Chapter 7 Solutions
Mechanics Of Materials - Si Version
- A steel pipe of 400-mm outer diameter is fabricated from 10-mm-thick plate by welding along a helix that forms an angle of 20°with a plane perpendicular to the axis of the pipe. Knowing that the maximum allowable normal and shearing stresses in the directions respectively normal and tangential to the weld are σ = 60 MPa and τ = 36 MPa, determine the magnitude P of the largest axial force that can be applied to the pipe.arrow_forwardA torque of magnitude T=12 kN·m is applied to the end of a tank containing compressed air under a pressure of 8 MPa. Knowing that the tank has a 180-mm inner diameter and a 12-mm wall thickness, determine the maximum normal stress and the maximum in-plane shearing stress in the tank.arrow_forward6. A strain gage located at C on the surface of bone AB indicates that the average normal stress in the bone is 3.80 MPa when the bone is subjected to two 1200-N forces as shown. Assuming the cross section of the bone at C to be annular and knowing that its outer diameter is 25 mm, determine the inner diameter of the bone’s cross section at C.arrow_forward
- The driveshaft of an automobile is being designed to transmit 238 hp at 3790 rpm. Determine the minimum diameter d required for a solid steel shaft if the allowable shear stress in the shaft is not to exceed 5700 psi.arrow_forwardShow that the angle between the plane of the major principal stress and the plane of the maximum shear stress is 45° for any state of stress.arrow_forwardTwo wooden planks, each 1212 in. thick and 9 in. wide, are joined by the dry mortise joint shown. Knowing that the wood used shears off along its grain when the average shearing stress reaches 1.8 ksi, determine the magnitude P of the axial load that will cause the joint to fail. The magnitude P of the axial load that will cause the joint to fail is kips.arrow_forward
- Straight rods of 0.30-in. diameter and 200-ft length are sometimes used to clear underground conduits of obstructions or to thread wires through a new conduit. The rods are made of high-strength steel and, for storage and transportation, are wrapped on spools of 5-ft diameter. Assuming that the yield strength is not exceeded, determine (a) the maximum stress in a rod, when the rod, which was initially straight, is wrapped on the spool, (b) the corresponding bending moment in the rod. Use E= 29 * 106 psi.arrow_forwardFor the state of plane stress shown, determine the largest value of σy for which the maximum in-plane shearing stress is equal to or less than 75 MPaarrow_forwardIn many situations it is known that the normal stress in a given direc-tion is zero. For example, σz= 0 in the case of the thin plate shown. For this case, which is known as plane stress, show that if the strains εx and εy have been determined experimentally, we can express σx, σyand εz as follows:arrow_forward
- Each of the four vertical Ilinks has an 8 x 36-mm uniform rectangular cross section and each of the four pins has a 16-mm diameter. Take P= 19 kN. 0.4 m C 0.25 m 0.2 m B. P Determine the average bearing stress at Bin member ABC, knowing that this member has a 10 x 50-mm uniform rectangular cross section. MPa. The average bearing stress at Bin member ABC is.arrow_forwardA centric load P is applied to the granite block shown. Knowing that the resulting maximum value of the shearing stress in the block is 2.5 ksi, determine (a) the magnitude of P, (b) the orientation of the surface on which the maximum shearing stress occurs, (c) the normal stress exerted on the surface, (d) the maximum value of the normal stress in the block.arrow_forwardA torque of 1.4KNm and two forces of 10kN and 12kN are applied to the top of a 65mm diameter solid steel post. Determine the principal stresses and the maximum shear stress at point H and point K.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