Concept explainers
A steel pipe of 12-in. outer diameter is fabricated from
Fig. P7.158
Fund the normal and in-plane shearing stresses, normal and tangential stress to the weld.
Answer to Problem 158RP
The normal stress in x-axis is
The normal stress in y-axis is
The shearing stress in xy-plane is
The normal stress in the weld is
The tangential stress in the weld is
Explanation of Solution
Given information:
The outer diameter of the steel pipe is
The thickness of the plate is
The plate makes an angle with plane perpendicular to the pipe is
The magnitude of the axial force P is 40 kips.
The torque applied in the pipe T is 80 kip-in.
Calculation:
Find the inner diameter of the steel
Substitute 12 in. for
Find the area of the steel pipe (A) using the equation.
Substitute 12 in. for
Find the polar moment of inertia (J) of the steel pipe using the equation.
Substitute 12 in. for
Find the normal stress
Substitute 40 kips for P and
The normal stress in x-axis is
The normal stress in y-axis is
Find the shearing stress
Substitute 80 kip-in. for T, 12 in. for
The shearing stress in xy-plane is
Show the stress element for pipe as in Figure 1.
Therefore,
The normal stress in x-axis is
The normal stress in y-axis is
The shearing stress in xy-plane is
Consider the axes
The normal stress in weld is
The shearing stress in weld is
Find the normal stress in the weld using the equation.
Substitute 0 for
Find the tangential stress in the weld using the equation.
Substitute 0 for
Show the stress element for weld as in Figure 2.
Therefore,
The normal stress in the weld is
The tangential stress in the weld is
Want to see more full solutions like this?
Chapter 7 Solutions
Connect 1-Semester Access Card for Mechanics of Materials
- An open-link chain is obtained by bending low-carbon steel rods of 0.5-in. diameter into the shape shown (Fig. ). Knowing that the chain carries a load of 160 lb, determine (a) the largest tensile and compressive stresses in the straight portion of a link, (b) the distance between the cen-troidal and the neutral axis of a cross sectionarrow_forwardAn offset h must be introduced into a metal tube of 0.75-in. outer diameter and 0.08-in. wall thickness. Knowing that the maximum stress after the offset is introduced must not exceed 4 times the stress in the tube when it was straight, determine the largest offset that can be used.arrow_forwardIn the structure shown, an 8 mm diameter pin is used at A, and 12 mm diameter pins are used at B and D. Knowing that the allowable shearing stress is 120 MPa at all connections and that the allowable normal stress and bearing stress is 240 MPa in each of the two links joining B and D, determine the allowable load Parrow_forward
- The steel pressure tank shown has a 750-mm inner diameter and a 9-mm wall thickness. Knowing that the butt-welded seams form an angle β= 50° with the longitudinal axis of the tank and that the gage pressure in the tank is 1.5 MPa, determine, (a) the normal stress per-pendicular to the weld, (b) the shearing stress parallel to the weld.arrow_forwardStraight 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_forwardA single horizontal force P with a magnitude of 150 lb is applied to end Dof lever ABD. Knowing that portion AB of the lever has a diameter of 1.2 in., determine (a) the normal and shearing stresses located at point H and having sides parallel to the x and y axes, (b) the principal planes and princi-pal stresses at point H.arrow_forward
- A composite shaft shown, composed of a steel (G = 77 GPa) core inside an aluminum (G = 25 GPa) jacket, carries a torque, T = 10 kN-m. The shaft is designed such that the aluminum jacket will fail first upon the application of the torque. 1) If the allowable shear strength of aluminum is 45 MPa, determine the minimum thickness, t, of the aluminum jacket, that can carry the torque.2) What must be the minimum shear strength of steel such that the aluminum jacket will fail first?3) Determine the maximum angle of twist that can be applied to the shaft.arrow_forwardDetermine the diameter of the largest circular hole that can be punched into a sheet of polystyrene 6 mm thick, knowing that the force exerted by the punch is 45 kN and that a 55-MPa average shearing stress is required to cause the material to fail.arrow_forwardProblem 1 A centric load P is applied to the granite block shown below. Knowing theresulting maximum value of the shearing stress in the block is 2.5 ksi, determine:The magnitude of PThe normal stress exerted on the surface where the shearing stress is the maximum valueThe maximum value of normal stressDraw an FBD showing the surface of maximum shearing stress, the maximum shearingstress and the normal stress occurring in that surface.arrow_forward
- A 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_forwardA flange coupling connects two 2 inch diameter shaft. The flanges are fitted by 6 bolts on a 7 “ bolt circle. If the shaft rotates at 300 rpm and transmit 45 hp, determine the required bolt diameter when allowable shear stress of 11,000 psi.arrow_forwardA load P is applied to a steel rod supported as shown by an aluminum plate into which a 0.6-in.-diameter hole has been drilled. Knowing that the shearing stress must not exceed 18 ksi in the steel rod and10 ksi in the aluminum plate, determine the largest load P that may be applied to the rod.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