Mechanics of materials assignment

ESC: 205 Mechanics of Materials Take-Home Test Freeman Spring 2014

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This take-home test is due on Thursday, May 1. Solutions will be available on Blackboard after

all tests are submitted. The Final Exam is Thursday, May 8. Please show all work. Neatness

counts!

Problem 1 (15 points)

Each nail can support a shear force 30 lb. What maximum spacing is required in each case if the

beam must support a vertical force of 100 lb. Where does the maximum shear stress on the beam

cross-section occur and what is it?

Problem 2 (15 points)

The state of plane stress at a point is shown on the element below. Determine the principal

stresses. Also determine the maximum in-plane shear stresses and the orientation of the element

upon which they act. Construct Mohr’s circle. Represent the state of stress on an element

oriented 30 o counterclockwise from the position shown.

Problem 3 (15 points)

An axial force of 300 lb and a torque of 25 lb-ft are applied to the shaft shown below. If the shaft

has a diameter of 1.5 in, determine the principal stresses and the maximum in-plane shear stress

at a point P on its surface. Construct Mohr’s circle.

?

80 MPa

MPa

10 MPa

ESC: 205 Mechanics of Materials Take-Home Test Freeman Spring 2014

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Problem 4 (15 points)

The 6061 T6 aluminum W10x39 member is to be used as a pin-connected column. Determine

the largest axial load it can support before it either begins to buckle or yield.

Problem 5 (15 points)

The beam is subjected to the load shown. Draw the shear and bending moment diagrams.

Determine the equations of the slope and elastic curve. EI is constant.

Problem 6 (25 points)

Determine the largest load of w that can be supported if the factor of safety with respect to

buckling of member AB is 2.5. Draw the shear and bending moment diagrams for the complete

length of beam BC. What is the maximum deflection? Assume that the structure is made of

2024-T4 aluminum and that AB is pinned at its ends for x-x axis buckling and fixed at its ends for

y-y axis buckling.

2.5 m

8 kN/m

20 kN-m

6 m 2 m

3 m