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 xx and yy axes. Find the minimum diameter required for the shaft if the maximum normal stress in the shaft cannot exceed 250 MPa250~ \text{MPa}. All dimensions are in mm\text{mm}.

Problem 2

The beam ABCDABCD shown in the figure is simply supported at AA and DD, and has a circular cross-section with a diameter of 80 mm80~\text{mm}. The distributed force acts at an angle of 60∘60^\circ to the ZZ axis and has components only along the ZZ and XX axis. The 1.2 kN1.2~\text{kN} force acts parallel to the ZZ axis and the 1.5 kN1.5~\text{kN} force acts parallel the XX axis. AB=0.6 mAB = 0.6~ \text{m}, BC=0.4 mBC = 0.4~ \text{m} and CD=1 mCD = 1~ \text{m}.

(a) Draw shear force and bending moment diagrams for the XYXY and YZYZ 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 mm35~\text{mm} in diameter, such that section A−CA-C is parallel to the yy-axis and section B−EB-E is parallel to xx-axis.

An unknown moment TT parallel to yy is applied at point AA, where there is also a spherical (ball) hinge, which constraints translations along xx, yy, and zz axes. The plane hinge at CC is contained in the x−zx-z plane, which means that it constrains translations along the xx and zz axes. The force of 1000 N1000~\text{N} at DD goes in −z-z, the force of 500 N500~\text{N} at DD goes in −y-y and the force of 500 N500~\text{N} at EE goes in −x-x. Given these conditions and the coordinate system provided, find:

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

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