ME 323: Mechanics of Materials

Fall 2021

Homework 1

Due Wednesday, September 1

Problem 1.1 (10 points)

ABCDE represents a frame attached to the wall at A. The free end (E) is subjected to two forces: 1) Pacting in the negative Z direction and 2) 2P acting in the positive X direction.

(a) Calculate the internal resultants, i.e, forces and moments developed at the centroid of cross sectionA

(b) Calculate the internal resultants, i.e, forces and moments developed at the centroid of cross sectionC

(c) Does the internal resultant force vary along the line segment AB? What about along line segmentBC?

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ME 323: Mechanics of Materials

Fall 2021

Homework 1

Due Wednesday, September 1

Problem 1.2(10 points)

A curved bar ABC is fixed to the wall at A and is subjected to two external forces at the free end, C : 1)P acting in the negative Y direction, and 2) Q in the positive X direction.

(a) Determine the internal resultant forces (normal and shear) and moments as a function of ✓ at B(acting at the centroid on the bar’s cross section).

(b) Using the equation developed in (a), calculate the internal moment at A (✓ = ⇡/2).

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ME 323: Mechanics of Materials

Fall 2021

Homework 1

Due Wednesday, September 1

Problem 1.3 (10 points)

Circular bar 1 is attached to the wall by brackets 2 and 3. Bracket 3 is supported by a pin joint at F.Bracket 2 is attached to bracket 3 by bolt assemblies.

Bar 1 is subjected to an external load of 5000 N (weight of the bar is negligible). Bracket 2 weighs 400 Nand bracket 3 weighs 300 N.

Bar 1 is made of a material which can withstand a maximum normal stress � =10 MPa and the boltedconnections are made of material which can withstand a maximum shear stress ⌧ =160 MPa. To avoidthe failure of the structure, determine:

(a) The smallest diameter of the bar AB.(b) The smallest diameters of the bolts at the joint C and D.

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ME 323: Mechanics of Materials

Fall 2020

Homework 1

Due Wednesday, January 27

Problem 1.4 Conceptual (2.5+2.5 points)

(a) The rod shown below has a rectangular cross section and is made of a material with Young’s

modulus E and positive Poisson’s ratio ⌫. It has dimensions L > b > h and it is subjected

to a tensile load P in the x direction, as shown.

Select the correct statement. And justify your stance.

(a) |�h| > |�b|(b) |�h| < |�b|(c) |�h| = |�b|(d) Insufficient information. Depends on the value of Poisson’s ratio.

(b) Bar ABC is supported by a pin joint at point A and loaded by a vertical force P at point

C. Bar ABC is also connected to bar BD via a pin joint at B which in turn is supported by

a pin joint at D. Bar BD is oriented along the x axis.

Select the zero internal resultant(s). And justify your stance.

(a) Normal force Fx

(b) Shear force Vy

(c) Bending moment Mz

(d) All internal resultants are non zero