CE 300 Term 07-1



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

PROBLEM SET #6 (50 points)

Due on the scheduled date for Lesson 22

1. (15 Points) Distributed Loads

Recently MAJ Hains inspected a dam and was concerned that erosion at the base of the dam is causing a dangerous condition. To mitigate the situation, he proposed that anchor rods be installed and that an extra ten feet of backfill be placed along the base of the dam.

Due to the damage, the support at the base of the dam is modeled as a pin. MAJ Hains already modeled the loads as shown below. The hydrostatic pressure due to the water is modeled as a triangular load and the backfill ground pressure is modeled as a quadrant of parabola.

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Part a. Determine the pin support reactions at the base of the dam and the tension in the anchor rod.

Part b. Design the anchor rod using Annealed Stainless Steel and a Factor of Safety of 2.5 with respect to the elastic strength. Rod sizes are available in ½ inch increments.

2. (15 Points) Centroids

COL Meyer is working on his latest carpentry project and needs to fabricate his own wooden T beams. He knows eventually he will conduct some design and analysis, so you will help him to determine the centroid for each beam configuration shown.

Remember, COL Meyer will be using dressed lumber, so refer to Table A-15 for actual dimensions.

Part a. For most of the T beams, COL Meyer will simply need to center a 2x12 on a 4x10 as shown to the right. Identify a reference point and calculate the location of the centroid for this composite beam.

Part b. Some of the beams will have to carry an extra load off-center, so COL Meyer will use a triangular steel stiffening plate as shown. The plate has a height of 6 inches, and the plate is flush with the edge. Identify a reference point and calculate the location of the centroid for this composite beam.

Part c. Finally, COL Meyer will need to pass wiring for his new entertainment center through a few of the beams. He will cut a 1.5 inch diameter hole, centered on the 4x10 piece of lumber. Identify a reference point and calculate the location of the centroid for this composite beam. (NOTE: This problem involves the subtraction of an area. For an example of the use of subtracted areas in centroid calculations, see Example 5-19 on page 218 of your textbook.)

3. (20 Points) Frame Analysis

Construction has begun on the Foley Center, which is a steel frame building. A sample of the plans is shown below.

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Erecting the Steel Frames.

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Part a. For the loading condition shown below, calculate the pin reactions at C and the force in the tie AB.

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Part b. The tie AB will actually be two rods connected together as shown below. Each rod will be connected with six bolts made of SAE 4340 heat-treated steel and will carry load in single shear. Using a factor of safety of 2.5 with respect to ultimate shear strength, what is the smallest diameter bolt size that can be used for the tie rod connections? Bolts are available in 1/16” increments of diameter.

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Part c. The tie rods will be made of a circular A36 steel bar. Design the tie using a Factor of Safety of 2.0. The tie is available in 1/16 inch increments.

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