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Homework 3 in MEE 322 Structural Mechanics | Normal and Shear Stresses Under Combined Loading Part 2

Problem 1

Three forces act on the tip of a L-shaped rod with a cross-sectional radius of 0.5 in.

(a) Determine the normal and shear stress at points A and B and draw the stress cube at those points based on the given coordinate system.

(b) Determine the maximum normal stress on the cross-section and locate the point at which it occurs.

Problem 2

The simply supported solid shaft has a radius of 15 mm and is under static equilibrium. Pulley C has a diameter of 100 mm. The pulleys B and D have the same diameter as each other. The forces on pulley B are at an angle of 45 to the negative z-axis. The forces on pulley C and pulley D are in the z and -y direction. The shaft dimensions are in mm.

(a) Determine the maximum bending and torsional stresses in the shaft.

(b) Locate the point(s) on the cross-section where the bending stress is maximum.

Problem 3

The structural part of a setup to measure net belt tensions in pulleys is shown in the figure. The belt tensions at both sides of the pulley at B (radius 10 cm) are P and F=0.1*P along z and a reaction force is measured from the pulley at C (radius 2 cm), which is connected to a load cell at E with an axial member parallel to x. Pulleys are rigidly attached to rod AD, which is made with a ductile steel rod 60 cm long and 1.27 cm in diameter. Length AB=0.20 m, and length DC=0.15 m. There is a spherical hinge at A and a plane hinge at D. The latter constrains motion in the x-z plane only.

(a) Draw bending moment and torsion diagrams for this structure as functions of the unknown tension P and use them to draw a diagram of the critical section showing internal loads (bending and torsion moments) and the critical points.

(b) Use your results from part a to determine the maximum normal stress due to bending and the maximum shear stress due to torsion in terms of the unknown tension P. Calculate the maximum value that P can have if only bending stresses are considered (with σallow = 350 MPa) and then if only torsion stresses are considered (with τallow = 175 MPa).

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Homework #2 in MEE 322 Structural Mechanics

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Homework 2 in MEE 322: Structural Mechanics | Normal and Shear Stress Under Combined Loading

Problem 1

The shaft with a circular cross-section is supported by two bearings at O and C. The bearings do not exert any moments or axial force on the shaft, and they act to constrain motion along the x and y axes. Find the minimum diameter required for the shaft if the maximum normal stress in the shaft cannot exceed 250~ \text{MPa}. All dimensions are in \text{mm}.

Problem 2

The beam ABCD shown in the figure is simply supported at A and D, and has a circular cross-section with a diameter of 80~\text{mm}. The distributed force acts at an angle of 60^\circ to the Z axis and has components only along the Z and X axis. The 1.2~\text{kN} force acts parallel to the Z axis and the 1.5~\text{kN} force acts parallel the X axis. AB = 0.6~ \text{m}, BC = 0.4~ \text{m} and CD = 1~ \text{m}.

(a) Draw shear force and bending moment diagrams for the XY and YZ planes.

(b) Determine the maximum tensile and compressive bending stress in the beam and show their locations on the cross-section of the beam.

Problem 3

The following steel structure will be made with a round bar 35~\text{mm} in diameter, such that section A-C is parallel to the y-axis and section B-E is parallel to x-axis.

An unknown moment T parallel to y is applied at point A, where there is also a spherical (ball) hinge, which constraints translations along x, y, and z axes. The plane hinge at C is contained in the x-z plane, which means that it constrains translations along the x and z axes. The force of 1000~\text{N} at D goes in -z, the force of 500~\text{N} at D goes in -y and the force of 500~\text{N} at E goes in -x. Given these conditions and the coordinate system provided, find:

(a) Diagrams of axial force, bending moment, and torsion moments for sections A-C and B-E. Use the given coordinate system to label the planes where you are making your internal reaction diagrams (x-y, x-z or z-y) and draw the corresponding axes.

(b) Calculate the maximum normal stress due to bending in this structure. Show in a diagram the point(s) in the cross-section of the structure where this stress occurs, and include the bending moments in each axis, the resultant moment, and the neutral axis. Use the given coordinate system to show the orientation of your diagram.

(c) Calculate the maximum shear stress due to torsion in this structure. Show in a diagram the point(s) in the cross-section of the structure where this stress occurs, including the torsion moment. Use the given coordinate system to show the orientation of your diagram.

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Homework 2 in MEE 322: Structural Mechanics

This is the complete solution manual to the problems in Homework 2 of ME322: Structural Mechanics. The 3 problems included in the manual are written above. The PDF document will be sent to your email address within 24 hours from the time of purchase. The email will be coming from [email protected] Do not forget to check on your spam folder. If you have not received your file in 24 hours, kindly send us an email at [email protected]

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