Note:
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In each project an explanation and general equations should be given.
Fields of applications with illustrative pictures.
O6U
MTE 108– Stress Analysis
Project # 1: Stress Analysis of Axial members
May, 2020
The horizontal rigid beam ABCD is supported by vertical bars BE and CF and is loaded
by vertical forces P1 = 400 kN and P2 = 360 kN acting at points A and D, respectively
(see figure). Bars BE and CF are made of steel (E = 200 GPa) and have cross-sectional
areas ABE = 11,100 mm2 and ACF = 9,280 mm2. Bars BE and CF have thickness of 37
mm and 32mm respectively. The distances between various points on the bars are shown
in the figure. A 10-mm-diameter pin is used at C and 8-mm-diameter pins are used at B
and E. The ultimate normal stress is 400 MPa in link BE and CF.
Required:
a) Draw the free-body diagram of the link ABC, and then calculate reactions at B and
C.
b) Calculate the axial stresses in the link BE and link CF far from Points B and C.
c) Calculate the axial stresses in the link BE and link CF at Points B and C.
d) Calculate the axial stain in links BE and CF.
e) Take Poisson’s ratio ν= 0.3, calculate the increase in the width of links BE and CF.
f) Determine the safety factor of links BE and CF at Pins B and C.
g) Determine the vertical displacements δA and δD of points A and D, respectively.
O6U
MTE 108 – Stress Analysis
Project # 2 : Stress Analysis of Shear members
May, 2020
Solve two problems
Problem #1: An angle bracket having thickness
t=12.7mm is attached to the flange of a column by
two 16 mm diameter bolts (see figure). A
uniformly distributed load acts on the top face of
the bracket with a pressure p=2 MPa. The top face
of the bracket has length L=152 mm. and width
b=63 mm. Determine the average bearing pressure
σb between the angle bracket and the bolts and the
average shear stress aver in the bolts. (Disregard
friction between the bracket and the column.)
Problem#2: A bolted connection between a
vertical column and a diagonal brace is shown in
the figure. The connection consists of three 16 mm
bolts that join two 6 mm end plates welded to the
brace and a 16 mm gusset plate welded to the
column. The compressive load P carried by the
brace equals 8.0 k. Determine the following
quantities:
(a) The average shear stress τaver in the bolts, and
(b) The average bearing stress σb between the
gusset plate and the bolts. (Disregard friction
between the plates.)
Problem #3: A steel plate of dimensions 2.5 x 1.2
x 0.1 m is hoisted by a cable sling that has a clevis
at each end (see figure). The pins through the
clevises are 18 mm in diameter and are located 2.0
m apart. Each half of the cable is at an angle of 32°
to the vertical. For these conditions, determine the
average shear stress τaver in the pins and the
average bearing stress σb between the steel plate
and the pins.
O6U
MTE 108 – Stress Analysis
Project # 3 : Stress Analysis of Trusses
May, 2020
The rigid bar EFG is supported by the
truss system shown. Knowing that the
members AE, AB, BF, BC, CF, CG, and
DE are solid circular rods of 17 mm.
Using E=70Gpa.
a) Determine the ground reactions at A
and D of structure.
b) Check the determinacy of the structure.
c) Determine the internal forces in the
members using Joint Equilibrium
method.
d) Determine the vertical deflection of point F caused by the applied load.
e) Determine the internal forces in members AE, AB and DE using the method of
sections
O6U
MTE 108 – Stress Analysis
Project # 4 : Stress Analysis of Torsional members
May, 2020
Two solid shafts (G=77 GPa) are connected by gears shown. A toque of magnitude
T=1000 N.m is applied at D as shown. Knowing that the diameter of shaft AB is 56 mm
and the diameter of shaft CD is 42 mm. The gear C radius is 40 mm and the gear B radius
is 100mm. The shaft CD length LCD= 500mm and the shaft AB length is LAB=400mm
determine:
a) The maximum shearing stress in shaft AB and shaft CD.
b) The angle of twist in shaft AB and shaft CD.
c) The total angle of twist at D.
O6U
MTE 108 – Stress Analysis
Project # 5 : Stress Analysis of Beams
May, 2020
The beam in the figure below is subjected to 10kN and 15kN vertical forces at points A
and E, uniformly distributed load with density 10kN/m. The cross-section of the beam is
shown to the right. Its dimensions are in mm.
a) Determine the reactions at the supports C and B.
b) Draw the Shear Force Diagram and Bending Moment Diagram.
c) Determine the cross-section area, the neutral axis and the second moment of area
about the neutral axis NA.
d) Calculate the stress due to bending at the point having maximum bending
moment. Plot the stress distribution through the cross-section.
e) Knowing that the allowable stress of the beam-material is allow = 150 GPa, is the
beam safe or not. If safe, determine the safety factor.