Mechanics of Deformable Bodies (Solved Problems)

Don Bosco Technical College College of Engineering

Mechanics of Deformable Bodies (12 Solved Problems)

Submitted by: Janray S. Rabaya Submitted to: Engr. King Howard A. Maneclang

CHAPTER 1 Stress Sample Problems 1.) The homogeneous bar AB weighing 1800 lb. is supported at either end by a steel cable. Calculate the smallest safe area of each cable if the working stress is 18 000 psi for steel. Solution:

2.) The homogeneous 6000-lb bar ABC is supported by a pin at C and a cable that runs from A to B around the frictionless pulley at D. Find the stress in the cable if its diameter is 0.6 in.

Solution:

3.) The uniform 300-lb bar AB carries a 500-lb vertical force at A. The bar is supported by a pin at B and the 0:5-in. diameter cable CD. Find the stress in the cable.

Solution:

CHAPTER 2 Sample Problems

Strain

1.) The rigid bar AB is supported by two rods made of the same material. If the bar is horizontal before the load P is applied, find the distance x that locates the position where P must act if the bar is to remain horizontal. Neglect the weight of bar AB. Solution:

2.) The rigid bars ABC and CD are supported by pins at A and D and by a steel rod at B. There is a roller connection between the bars at C. Compute the vertical displacement of point C caused by the 50-kN load. Solution:

3.) A uniform bar of length L, cross-sectional area A, and mass density r is suspended vertically from one end. (a) Show that the elongation of the bar is d ¼ rgL2=ð2EÞ, where g is the gravitational acceleration and E is the modulus of elasticity. (b) If the mass of the bar is M, show that d ¼ MgL=ð2EAÞ. Solution:

CHAPTER 3 Torsion

Sample Problems 1.) The steel shaft, 3 ft long and 4 in. in diameter, carries the end torque of 15 kip _ ft. Determine (a) the maximum shear stress in the shaft; and (b) the angle of twist of the shaft. Use G ¼ 12 _ 106 psi for steel. Solution:

2.) The 16-ft solid steel shaft is twisted through 4_. If the maximum shear stress is 8000 psi, determine the diameter d of the shaft. Use G ¼ 12 _ 106 psi for steel. Solution:

3.) The compound shaft consists of bronze and steel segments, both

having 120-mm diameters. If the torque T causes a maximum shear stress of 100 MPa in the bronze segment, determine the angle of rotation of the free end. Use G ¼ 83 GPa for steel and G ¼ 35 GPa for bronze. Solution:

CHAPTER 4 Shear and Moment in Beams Sample Problems

1.) For the beam shown, derive the expressions for V and M, and draw the shear force and bending moment diagrams. Neglect the weight of the beam. Solution:

2.) For the beam shown, derive the expressions for V and M, and draw the shear force and bending moment diagrams. Neglect the weight of the beam.

Solution:

3.) Construct the shear force and bending moment diagrams for the beam shown by the area method. Neglect the weight of the beam.

Solution: