CE 300 AY 07-1 (Distance Education Pilot Project) 15 September 2006

PROBLEM SET #4 (50 points)

Due on the scheduled date for Lesson 13

JEFFERSON HALL CONSTRUCTION CONTINUES!

1. (20 Points) Trusses, Stress and Strain

You have been asked to continue the analysis of the boom of the crane on the Jefferson Hall jobsite that you started in Problem Set #3. All members of the truss are solid rectangular members made of 2014-T4 Aluminum (see Appendix A-17) with an area of 2.0 in2 (see diagram below). Note that the support reactions at A and the tension in the cable at L have been provided for you!

Determine the following:a. The maximum normal stress in members CT and BC of the bridge. State if theses

stresses are still in the elastic region and justify why or why not.b. The corresponding maximum shear stress in members CT and BC.c. The normal strains in members CT and BC.d. The corresponding normal deformation of members CT and BC.e. The change in the lateral dimensions (width and height) of member CT if Poisson’s

ratio for this Aluminum is 0.25.

15o

A

PQ

IHGFEDCB

LMN

K

O

J

FCABLE = 19641 lbU T S R

10 bays at 6 ft each = 60 feet80 lb 80 lb 80 lb 80 lb 80 lb 80 lb 80 lb 80 lb 80 lb

5000 lb

480 lb

4 ft

Ax = 18972 lb

Ay = 1116 lb

Figure 4.1 Crane Boom Configuration

1 in.

2.0 in.

1 in.Figure 4.2 Truss Member Dimensions

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2. (15 Points) Shear Stress

The crane on the Jefferson Hall jobsite has a connection in the main cable to allow different lower cable units to be attached, depending on what needs to be lifted. To enable the construction crews to swap out cables a quick release pin is used in the connection between the main cable of the crane and the lower cable unit as shown below.

Cable Connection

http://www.library.usma.edu/jeffhall/construction.aspAccessed 05 September 2006

a. Identify the type of shear (single or double) that the pin connecting the cables is undergoing.

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MAIN CABLE

LOWER CABLE UNIT

PIN

5000 lb

b. Compute the shear stress in the pin if the pin has a diameter of 0.5 inches. If the pin is made of wrought iron, will it be up to the task (i.e. is it acceptable in shear?). Justify your answer.

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3. (15 Points) Material Properties

The main cable of the crane needs to be replaced and ordering a new cable will take too long. There is some unknown material on-hand that looks like it may be able to be used for replacing the main cable. However, before you utilize the material, you need to know its material properties. Naturally, you conduct a tension test on a sample based on your CE300 experience. The sample has a diameter of 9.54 mm and a gage length of 50 mm. Your test data is below: (this data will also be posted on BlackBoard).

Data Point Load (kN) Deformation (mm)1 0 02 1.4 0.0053 3 0.014 4.4 0.0155 6 0.026 7.5 0.0257 8.8 0.038 11.7 0.049 14.6 0.05

10 17.8 0.0711 18 0.2512 17.7 0.513 18.1 114 18 315 17.9 616 18 817 19 1018 23 1219 30.4 1520 32.5 1721 23.4 20

a. Using Excel, process (and print out) this data for stress and strain and plot (and print out) a complete stress-strain curve for the unknown material. Show your calculations for stress and strain for Data Point 2 (the 1.4 kN load and 0.005 mm deformation).

b. On the stress-strain curve from Part a, label the elastic, yielding, strain hardening and necking regions and determine and label the ultimate and fracture strengths.

c. Plot a second stress-strain curve with just the first 11 data points (0 kN to 18 kN). On this curve determine and label the yield strength (by the 0.2% offset method) and the modulus of elasticity. Show your calculation for the modulus of elasticity.

d. Based on your results, what type of material do you think you are working with and why?

Remember to print out the processed data and the two plots and to document appropriately! Also, show your calculations for stress and strain for Point 2 and the modulus of elasticity.

Show all work on the plots!

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