University of Florida/Egm3520/Mom-s13-team4-R5
Report 5
Problem 5.1
editP4.7, Beer 2012
Problem Statement
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Two W4x13 rolled sections are welded together as shown. For the steel alloy used: , and a factor of safety of 3.0
Objective
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Determine the largest couple that can be applied when the assembly is bent about the z axis.
Solution
editStep 1
editDraw dimensions from appendix C.
Step 2
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From appendix C for W4x13:
The area is equal to
The moment of inertia about x is equal to
The base is equal to
Step 3
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The parallel axis theorem gives us the following
being the moment about the neutral axis
Solving for the moment of inertia about the neutral axis, we find
Since there are two sections and the moment of inertia of the two sections about the neutral axis is
Step 4
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Allowable stress is equal to the ultimate stress divided by the factor safety
Step 5
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The largest couple that can be applied when the assembly is bent about the z axis is 1259 kip*in
Honor Pledge
editOn our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.
Problem 5.2
editP4.8, Beer 2012
Problem Statement
edit
Two W4x13 rolled sections are welded together as shown. For the steel alloy used: , and a factor of safety of 3.0
Objective
edit
Determine the largest couple that can be applied when the assembly is bent about the z axis.
Solution
editStep 1
editDraw dimensions from appendix C.
Step 2
edit
From appendix C for W4x13:
The area is equal to
The moment of inertia about y is equal to
The base is equal to
Step 3
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Allowable stress is equal to the ultimate stress divided by the factor safety
Step 4
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The parallel axis theorem gives us the following
being the moment about the neutral axis
Solving for the moment of inertia about the neutral axis, we find
Since there are two sections and the moment of inertia of the two sections about the neutral axis is
Step 5
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The largest distance from from the centroid to either side is
The largest couple that can be applied when the assembly is bent about the z axis is 187.1 kip*in
Honor Pledge
editOn our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.
Problem 5.3
editP4.13, Beer 2012
Problem Statement
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A beam of the cross section shown is bent about a horizontal axis and that the bending moment is 6 kN*m.
Objective
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Determine the total force acting on the shaded portion of the web.
Solution
editStep 1
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To determine the total force acting on the shades area
we need to find the distribution of throught the shades area
the distribution would be:
Step 2
editWe have
and
the centroidal Moment of Inertia is
then
Honor Pledge
editOn our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.
Problem 5.4
editP4.16, Beer 2012
Problem Statement
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The beam shown is made of a nylon for which the allowable stress is 24 MPa in tension and 30 MPa in compression.
Objective
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Determine the largest couple M that can be applied to the beam for
Givens
editb = 40mm
s = 15mm
d = 30mm
h = d-s = 15mm
t = 20mm
=?
=?
Solution
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Step 1
editIn order to find the Neutral Axis, we must find the centroid of the T-shape cross-section
Step 2
editNow We solve for
Step 3
editNow we must solve for the Moment of Inertia of the T Shape:
Step 4
editWe can calculate the maximum tensile strength, given that our maximum compression stress is 30Mpa.
Step 5
editSince , the maximum stress is seen through compression. Therefore, we will use that compression stress in the elastic flexural formula:
Step 6
editTherefore, the largest couple moment that can be applied to the beam is as follows:
Honor Pledge
editOn our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.
Problem 5.5
editP4.20, Beer 2012
Problem Statement
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The extruded beam shown has allowable stress is 120 MPa in tension and 150 MPa in compression.
Objective
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Determine the largest couple M that can be applied.
Solution
editStep 1
editThe centroid of a trapezoid is given by
where a = 80 mm, b = 40 mm, and h = 54 mm
so
Step 2
editSplitting the trapezoid into 2 triangles and a rectangle we can find the Moment of inertia of the trapezoid by
summing the individual moments of inertia.
Step 3
editThe moment of inertia of the triangle is given by:
The Area of the triangle is:
centroid of a triangle is : y =
so dy = 36mm - 30mm = 6mm
Step 4
editThe moment of inertia of the rectangle is given by:
The Area of the rectangle is:
the centroid of a rectangle is the center so y = 27 mm
so dy = 30 mm - 27 mm = 3 mm
Step 5
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Step 6
editApplying the Elastic fexural formula to get:
Looking at the bottom half of the beam gives us c = 30 mm and
Looking at the top half of the beam gives us c = 24 mm and
The larges couple M is felt by the bottom half
Honor Pledge
editOn our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.
Problem 5.6
editP3.53, Beer 2012
Problem Statement
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The solid cylinders AB and BC are bonded together at B and are attached to fixed supports at A and C. The modulus of rigidity is for aluminum and for brass.
Objective
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Determine the maximum shearing stress (a) in cylinder AB, (b) in cylinder BC.
Solution
editFBD
We need to split the solid shaft AC into two free body diagrams, shaft AB and shaft BC
Given
Step 1
editIn order to find the max shearing stress, we need to determine the Torques at point A and C
Step 2
editFind the moment of inertia in each cylinder
Step 3
editFind the max sheer stress in each cylinder
Honor Pledge
editOn our honor, we did not do this problem on our own, without looking at the solutions in previous semesters or other online solutions.