Name:
Date:
Subject and Section:
Permit No.:
Student No.:
Problem Set 1 | Mechanics of Deformable Bodies
Instructions: Write your solutions, neatly and organized on a long bond paper with border. Margin is
0.5” on all sides. Write your name on the upper right corner of each page. Box your answers, must
include units, 3 decimal places. To be submitted on August 5,2024 3 pm.
Situation 1. Two vertical forces are applied to a beam of the cross section shown. Determine the
maximum tensile and compressive stresses in portion BC of the beam.
_________________1. Maximum tensile stress.
_________________2.Maximum compressive stress.
Situation 2. Two vertical forces are applied to a beam of the cross section shown. Determine the
maximum tensile and compressive stresses in portion BC of the beam.
_________________3.Maximum tensile stress.
_________________4.Maximum compressive stress.
Situation 3. Knowing that a beam of the cross section shown is bent about a horizontal axis and that
the bending moment is 50 kip ⋅ in., determine the total force acting: (hint : σ = F/A = My/I )
_________________5.on the top flange.
_________________6.on the shaded portion of the web.
_________________7. For the beam and loading shown, determine the maximum normal stress due
tobending on a transverse section at C.
_________________8. Determine the maximum normal stress due to bending or the beam and loading
shown.power that can be transmitted.
Situation 5. Three shafts and four gears are used to form a gear train that will transmit 7.5 kW from the motor at
A to a machine tool at F. (Bearings for the shafts are omitted in the sketch.) Knowing that the frequency of the
motor is 30 Hz and that the allowable stress for each shaft is 60 MPa, determine the required diameter of each
shaft.
_________________10. AB
_________________11.DC
_________________12.EF
_________________13.A 1.5-m-long solid steel of 48 mm diameter is to transmit 36 kW between a motor and a
machine tool. Determine the lowest speed at which the shaft can rotate, knowing that G=77.2 GPa, that the
maximum shearing stress must not exceed 60 MPa, and the angle of twist must not exceed 2.5°.
Situation 6. A 90-N ⋅ m torque is applied to a hollow shaft having the cross section shown. Neglecting the
effect of stress concentrations, determine the shearing stress at:
_________________14.point a.
_________________15.point b.
Situation 7. Two solid steel shafts (G = 77.2GPa) are connected to a coupling disk B and to fixed supports at A
and C. For the loading shown, determine:
_________________16.the reaction at each support A.
_________________17.the reaction at each support C.
_________________18.the maximum shearing stress in shaft AB
_________________19.the maximum shearing stress in shaft BC.
angle of twist of the shaft not exceed 4° when a torque of 750 N ⋅ m is applied. Determine the required
_________________20.The design specifications of a 1.2-m-long solid transmission shaft require that the
diameter of the shaft, knowing that the shaft is made of a steel with an allowable shearing stress of 90 MPa
and a modulus of rigidity of 77.2 GPa.
