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assn2 (1)

# assn2 (1) - 1.050 Dimension Analysis(HW#2 Due MIT...

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1.050: Dimension Analysis (HW #2) Due: September 19, 2007 MIT – 1.050 (Engineering Mechanics I) Fall 2007 Instructor: Markus J. BUEHLER Team Building and Team Work: We strongly encourage you to form Homework teams of three students. Each team only submits one solution for correction. We expect true team work, i.e. one where everybody contributes equally to the result. This is testified by the team members signing at the end of the team copy a written declaration that "the undersigned have equally contributed to the homework". Ideally, each student will work first individually through the homework set. The team then meets and discusses questions, difficulties and solutions, and eventually, meets with TA or instructor. Important: Specify all resources you use for your solution. The following set of exercises is designed to train you in the use of dimensional analysis. 1. A vertical excavation : Consider a vertical excavation of a cohesive soil with strength σ 0 . (a) Using dimensional analysis, determine how deep can one cut into the soil before it collapses under the action of its own weight. What type of information does dimensional analysis provide at the end of the analysis? Comment. (b) One O’Fifty Engineering Consultants have run an excavation experiment and determined the following properties for soil MIT1050: ρ = 2.4 g / cm 3 σ 0 = 10 kPa h = 0.425 m Using this data, could one determine explicitly the relation between the height of the excavation and the strength and weight of the soil wall? (c) Your 1.050 TA run some soil tests and determined the following properties for two soil types: clay : σ 0 = 30 kPa , ρ = 1.7 g / cm 3 sand : σ 0 = 3 kPa , ρ = 1.4 g / cm 3 Based on your dimensional analysis results and the experimental data from One O’Fifty Engineering Consultants, determine the heights of excavation if you were working on those two types of soils. Comment on your results.

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Due: Wednesday – September 19, 2007 (In class) Page 2 of 7 h g r ρ before excavation after excavation 2. ‘D-Analyzing’ a record-breaking suspension bridge: Civil engineers are currently working on the design of an intercontinental bridge across the Red Sea, providing ground transportation between the Arabian Peninsula and the Horn of Africa. Upon successful
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assn2 (1) - 1.050 Dimension Analysis(HW#2 Due MIT...

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