Concept explainers
(a)
The points where the shearing stress is maximum and the values of the stress.
(a)

Answer to Problem 80P
The shearing stress is maximum at the points of
The maximum shear stress along the vertical leg is
The maximum shear stress along the horizontal leg is
The maximum shear stress at the corner of the leg is
Explanation of Solution
Calculation:
Refer to sample problem 6.6 in the text book.
Combined stress along the vertical leg
Combined stress along the horizontal leg
Modify Equation (1).
Calculate the point along the vertical leg differentiate both sides of the equation with respect to y as shown below.
Consider the condition
Hence, the shearing stress is maximum at the points of
Calculate the maximum shear stress along the vertical leg as shown below.
Substitute
Hence, the maximum shear stress along the vertical leg is
Modify Equation (2).
Calculate the point along the horizontal leg differentiate both sides of the equation with respect to z as shown below.
Consider the condition
Hence, the shearing stress is maximum at the points of
Calculate the maximum shear stress along the horizontal leg as shown below.
Substitute
Hence, the maximum shear stress along the horizontal leg is
The corner points of the horizontal and vertical legs are
Calculate the maximum shear stress at the corner point as shown below.
Substitute 0 for y in Equation (1).
Substitute 0 for z in Equation (2).
Therefore, the maximum shear stress at the corner of the leg is
(b)
Show that the points are located on the neutral axis for the loading P.
(b)

Answer to Problem 80P
The points y and z are located on the neutral axis for the loading P.
Explanation of Solution
Calculation:
Sketch the cross section along the neutral axis as shown below.
Refer to Figure 1.
Calculate the moment of inertia as shown below.
Along
Along
Consider the angle
Calculate angle
Substitute
Calculate the angle of the neutral axis from the horizontal as shown below.
Calculate the location of the centroid as shown below.
Along y axis:
Along z axis:
Calculate the neutral axis intersects for vertical leg as shown below.
Substitute
Calculate the neutral axis intersects for horizontal leg as shown below.
Substitute
Therefore, the points y and z are located on the neutral axis for the loading P
Want to see more full solutions like this?
Chapter 6 Solutions
EBK MECHANICS OF MATERIALS
- Air enters the compressor of a regenerative gas turbine engine at 310 K and 100 kPa, where it is compressed to 900 kPa and 650 K. The regenerator has an effectiveness of 75%, and the air enters the turbine at 1400 K. Assume variable specific heats for air. For a turbine efficiency of 90 percent, determine the amount of heat transfer in the regenerator. The amount of heat transfer in the regenerator is kJ/kg.arrow_forwardAir enters the compressor of a regenerative gas turbine engine at 310 K and 100 kPa, where it is compressed to 900 kPa and 650 K. The regenerator has an effectiveness of 79 percent, and the air enters the turbine at 1400 K. Assume constant specific heats for air at room temperature. The properties of air at room temperature are cp = 1.005 kJ/kg·K and k = 1.4. For a turbine efficiency of 90 percent, determine the amount of heat transfer in the regenerator. The amount of heat transfer in the regenerator is kJ/kg.arrow_forwardHints: Find the closed loop transfer function and then plot the step response for diFerentvalues of K in MATLAB. Show step response plot for different values of K. Auto Controls Show solutions and provide matlab code NO COPIED ANSWERS OR WILL REPORT!!!! Use own solutionarrow_forward
- what is shear stress and normal? how to tell them while calculating?arrow_forward12 mm 45 mm 20 kN 20 kN 12 mm 45 mm PROBLEM 1.61 For the assembly and loading of Problem 1.60, determine (a) the average shearing stress in the pin at C, (b) the average bearing stress at C in member BC, (c) the average bearing stress at B in member BC. PROBLEM 1.60 Two horizontal 20-kN forces are applied to pin B of the assembly shown. Knowing that a pin of 20-mm diameter is used at each connection, determine the maximum value of the average normal stress (a) in link AB, (b) in link BC.arrow_forwardHow do you find these answers?arrow_forward
- 250 mm 400 mm A B C E F 250 mm PROBLEM 1.52 Each of the two vertical links CF connecting the two horizontal members AD and EG has a 10 × 40-mm uniform rectangular cross section and is made of a steel with an ultimate strength in tension of 400 MPa, while each of the pins at C and F has a 20-mm diameter and are made of a steel with an ultimate strength in shear of 150 MPa. Determine the overall factor of safety for the links CF and the pins connecting them to the horizontal members. 24 kNarrow_forward50 mm 12 mm B O C OA 300 mm 450 mm E PROBLEM 1.51 Each of the steel links AB and CD is connected to a support and to member BCE by 25-mm-diameter steel pins acting in single shear. Knowing that the ultimate shearing stress is 210 MPa for the steel used in the pins and that the ultimate normal stress is 490 MPa for the steel used in the links, determine the allowable load P if an overall factor of safety of 3.0 is desired. (Note that the links are not reinforced around the pin holes.)arrow_forward3. A 15% magnesium chloride solution is flowing through a 5-nom sch 40 commercial steel pipe at a rate of 325,000 lbm/h. The average temperature of the magnesium chloride solution as it flows through the pipe is 10°F. Determine the convective heat transfer coefficient inside the pipe.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





