University of Florida/Egm3520/s13.team4.r2

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Report 2

Problem 2.1[edit]

Pb-9.1 in sec.9.

Indented line

Problem Statement[edit]

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[edit]


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[edit]

P2.12, Beer 2012

Problem Statement[edit]

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[edit]

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[edit]

P2.16, Beer 2012

Problem Statement[edit]

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[edit]

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[edit]

P2.24, Beer 2012

Problem Statement[edit]

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[edit]

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[edit]

P2.40, Beer 2012

Problem Statement[edit]

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[edit]

PROBLEM 2-40

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[edit]

P2.44, Beer 2012

Problem Statement[edit]

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[edit]

2.44 image 1












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