CE 300 AY 07-1 (Distance Education Pilot Project) 20 September 2006
PROBLEM SET #5 (50 points)
Due on the scheduled date for Lesson 16
JEFFERSON HALL CONSTRUCTION CONTINUES!
1. (25 Points) Tension Member Design and Analysis
To finish up the analysis of the crane on the Jefferson Hall Construction site, you have been assigned the task of analyzing and designing the main cable.
Part a. Based on the 5000 lb load due to the pipes, determine if the current cable, consisting of 12 strands of structural steel wire each 0.5 inch in diameter, is adequate to carry the load with a Factor of Safety of 15 with respect to the elastic strength.
Part b. The pipes need to be placed in a tight spot, so the cable, which is 120 feet long, cannot elongate more than 1 inch. If the change in temperature on the day the pipes are placed is expected to be 60oF, what will be the total axial deformation and will this exceed the allowable 1 inch elongation?
Part c. The cable is closing in on the end of its expected lifespan and needs to be replaced. Wrought Monel wire strands each 0.75 inch in diameter are being considered. Determine how many strands are needed to carry the 5000 lb pipe load and achieve the desired Factor of Safety of 15 with respect to the elastic strength.
Part d. The contractor wants to know which is the better value, the 12 strand structural steel cable, ($0.75 per pound) or the Monel cable you designed in Part c, ($1.25 per pound). Determine which cable is the better value to replace the 120 feet of cable needed.
HINT: Check Table A-17 for useful material properties.
2. (25 Points) Truss Design and Analysis
As part of your plan to show the new “Supe” your school spirit, in preparation for the big game against Notre Dame, you are planning to install a large “Go Army, Beat Navy” sign on the Pratt Deck Truss bridge shown below near Annapolis, Maryland.
Figure 1. Pratt Deck Truss Bridge
During your initial recon of the bridge over Labor Day Weekend, you are able to meet with a the local engineer and find out that the total load on the bridge, to include the self-weight of the members, deck and traffic loads, is modeled as 10 kip loads on the top joints as shown in Figure 2.
Figure 2. Sketch of Deck and Traffic Loads
You decide that for the sign, the bigger, the better and plan to use a 24 foot wide sign made of aluminum which you plan to hang from joints K and I. The combined weight of your “Go Army” sign and the cables to attach it to joints K and I is 8000 lb and you know that the weight is evenly distributed between the two joints.
All members of the bridge have the following cross-section as shown in Figure 3.
Figure 3. Member Cross-section
Part a. For this loading condition determine which of members CD, CJ, or JK is the critical member and justify why you think it is the critical member. (Ignore buckling when making this comparison).
Part b. Though you want to show your school spirit, you also don’t want to end up in the newspaper for causing a bridge failure. Based on a hasty Risk Assessment, you determine that you want to maintain a Factor of Safety of 3.5 with respect to the elastic strength. All members of the bridge are made out of malleable cast iron.
Determine the actual Factor of Safety with respect to yielding for axial loading based for the critical member you found in Part a. Does this actual factor of safety meet your desired Factor of Safety, or should you reconsider changing the size of your sign?
Part c. Unfortunately one of your cohorts already ordered the sign before you completed your analysis. Now that you’ve spent all of your Cow Loan on this spirit mission, you are bound to complete the mission. You decide that all you need to do to make the sign work for your desired factor of safety is to replace member CD. You query local vendors and determine that the only available sections are solid circular structural steel (A36) bars available in half inch diameter increments.
Design member CD for a Factor of Safety of 3.5 with respect to the elastic strength based on the load condition from Part a, (i.e. you don’t need to recalculate the force in the member), and select the appropriate size bar.
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