University of Florida/Egm3520/s13.team4.r2

Report 2

Problem 2.1

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Pb-9.1 in sec.9.

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Problem Statement

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1)Solve for the reactions at B and at A in the Example 2.04 (see textbook page 72) with the stress strain relation  
2)Do the results depend on the length of each segment and the Young's modulus?


Solution

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problem 2.04, Beer 2012 p.72


Given:

Length

 
 


Area

 
 

Young's modulus

 


Applied forces

 
 


Draw a Free Body Diagram for each section

 
2.04 problem, Vu-Quoc sec.9 p.9-6

Use   on FBD 3

 

Knowing that the strain relation is found by:

 

We understand that without a linear strain relation we can't use the superposition principle to separate the reaction as we did in class.
So we'll need to set two FBD's displacement equations equal to each other in order to solve


The displacement equation mentioned previously is applied to FBD 3, which yeilds:

 

To solve for   we must sum all displacements from each section we cut and set it equal to 0

These equations yield

 

 

 

 


 


 


since all quantities are squared, therefore

 

 

 

 


 

 

 

 


 

 

 

 

 


 
Solution 2.04

Problem R2.2

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P2.12, Beer 2012

Problem Statement

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A nylon thread is to be subjected to a 10-N tension. Knowing that E = 3.2 GPa, that the maximum allowable normal stress is 40 MPa, and that the length of the thread must not increase by more than 1%, determine the required diameter of the thread

Solution

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GIVEN:

 

 

 


WE KNOW THAT

 

AND IT IS REQUIRED THAT

 


 

 

 

AND WE ALSO KNOW THAT  

SO  

 

 

 

 


On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.

Problem R2.3

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P2.16, Beer 2012

Problem Statement

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The brass tube AB (E = 105 GPa) has a cross-sectional area of 140 mm^2 and is fitted with a plug at A. The tube is attached at B to a rigid plate that is itself attached at C to the bottom of an aluminum cylinder (E = 72 GPa) with a cross-sectional area of 250 mm^2. The cylinder is then hung from a support at D. In order to close the cylinder, the plug must move down through 1 mm. Determine the force P that must be applied to the cylinder.

Solution

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Given: Brass Tube AB:  

 

 

Aluminum Cylinder DC:

 

 

 

Equations: Compression of Brass Tube AB:  

Tension of Aluminum Cylinder DC:  

We know the total deflection:

 

 

 


On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.

Problem R2.4

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P2.24, Beer 2012

Problem Statement

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For the steel truss (E = 29 x 10^6 psi) and loading shown, determine the deformations of members BD and DE, knowing that their cross-sectional areas are 2 in^2 and 3 in^2, respectively.

Solution

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Free Body Diagrams


 


 


 


 


 


 


 



On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.

Problem R2.5

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P2.40, Beer 2012

Problem Statement

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A polystyrene rod consisting of two cylindrical portions AB and BC is restrained at both ends and supports two 6-kip loads as shown. Knowing that E = 0.45 X 10^6 psi, determine (a) the reactions at A and C, (b) the normal stress in each portion of the rod.

Solution

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Splitting the diagram into two parts we get part 1 and part 2 So we are given:

Part 1:

 

 

Part 2:

 

 


 

 

 


Looking at the free body diagram we see that


 


The total   equals zero so


 


Using the formula


 


We find that


 


Substituting in the reaction forces   and  


  will show negative because the force is facing opposite to  


 


Solving for   we get


 

So


  and solving a system of equations with

  Gives

 
 

(b) Using the formula  

So


 
 


On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.

Problem R2.6

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P2.44, Beer 2012

Problem Statement

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The rigid bar AD is supported by two steel wires of 1 16-in. diameter (E = 29 X 10^6 psi) and a pin and bracket at D. Knowing that the wires were initially taut, determine (a) the additional tension in each wire when a 120-lb load P is applied at B, (b) the corresponding deflection of point B.

Solution

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On our honor, we did this assignment on our own, without looking at the solutions in previous semesters or other online solutions.