ME 323: Mechanics of Materials

Spring 2021

Homework 7

Due Friday, March 26

Problem 7.1 (10 points)

A rigid bar BF is welded (fixed attachment) to an elastic cantilever beam ABC at location B as shown in

the figure below. The cantilever beam has elastic modulus E and second moment of area I. A point load

P is applied at F. Using the second order integration method:

1. Calculate the deflection at the free end vD in terms of P, L, E and I.

2. Plot the deflection of the beam ABC. Non-dimensionalize the plot, i.e., x becomes x/L and deflection

v becomes v/|vD| where |vD| is the magnitude of deflection at free end D.

3. Does the maximum deflection, in absolute value, occur at free end D? (Answer Yes or No using the

plot developed)

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ME 323: Mechanics of Materials

Spring 2021

Homework 7

Due Friday, March 26

Problem 7.2 (10 points)

A cantilever beam ABCD with square cross section (6" x 6") has a roller support at the free end at D

and it is subjected to a uniformly distributed load (100 lb/ft) between B and C. Using second order

integration method:

(a) Determine the reactions at A and D.

(b) Plot the deflection of the beam ABCD (similar to P7.1).

(c) Does the maximum deflection, in absolute value, occur exactly at the center? (Answer Yes or No

using the plot developed).

Data: E = 30,000 ksi, I = 108 in4.

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ME 323: Mechanics of Materials

Spring 2021

Homework 7

Due Friday, March 26

Problem 7.3 (10 points)

A cantilever beam ABC with a circular cross section has a roller support at B and is subjected to a

uniformly distributed load w0 between B and C, a concentrated load P at C, and an external couple M0

at B. Using the superposition principles, determine:

(a) The reaction at point B.

(b) The analytical expression for the deflection of the beam vx(c) The deflection at point C.

Data: L1 = 1 m, L2 = 2 m, d = 40 mm, E = 200 GPa, P = 150 N, M0 = 100 N.m, and w0 = 80 N/m.

Note: Please refer to the attached table for the necessary beam deflection equations.

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ME 323: Mechanics of Materials

Spring 2021

Homework 7

Due Friday, March 26

Problem 7.5 (2.5 + 2.5 points)

1. Choose the schematic that depicts the deflection curve of the beam shown below. Briefly justify your

choice.

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ME 323: Mechanics of Materials

Spring 2021

Homework 7

Due Friday, March 26

2. The beam shown below is fixed to a wall at A and supported by a roller at C. If the beam is subjected

to an external couple MC at C.

Indicate which of the following statements are true. Briefly justify your choice.

(a) Only the slope is continuous at C.

(b) Only the deflection is continuous at C.

(c) The slope and deflection are both continuous at C.

(d) The slope and deflection are both continuous at C, and the deflection must be equal to zero at

C.

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