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Flexible Cables -and- Exam #2 Updates -and- Buoyancy ENGR B36 - Statics Pat Aderhold 11/17/2014 Exam #2 Adjustment • Sample solution on white board • Rubric Free body diagram(s) 10 pts Demonstrate CD 2 force member 3 Equilibrium equations 10 Solution for force on CD 5 Solution for reactions at A 7 Quiz #4 Exam #2 Adjustment • Originally: Average - 67.4% Problem 1 Avg. - 49% Problem 2 Avg. - 83% Problem 3 Avg. - 72% • On “Quiz #4”: 26.9/35.0 = 77.0% Promised ½ points back on worst problem Given 75% back Exam #2 Adjustment • Adjusted Average: 75.5% • Grade Breakdown A ----------- 3 B ----------- 14 C ----------- 6 Below ------- 7 Other Thoughts on Exams • Bring a straight-edge • First draft on a separate page? • More linear, top-to-bottom Will try to target specific concepts for Exam #3 Shear & Moment Diagrams • Practice Problem Solutions posted (x2) • Won’t put complicated one on exam Varying distributed load Non-linear Unique supports • Will probably see simple version on Exam #3 Concentrated and constant, distributed loads Simple supports • Might see some “tricky” features Overhang beyond supports Loading “down” at supports or “up” along span of beam Fluid Statics • Question over last Wednesday’s material? • Did you try practice problems yet? {189, 199, 210} • Didn’t have time for Buoyancy Fluid Statics - Buoyancy • Cut a hole in the water • Replace it with lighter object • Surrounding fluid pushes up on object Fbuoyancy = rsurrounding _ fluid × g ×Vsubmerged Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 312 Practice Problem 5/198 g = rg g oil = 56 lb ft 3 g water = 64 lb 3 ft g wood = 50 lb 3 ft h=? Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 320 Flexible Cables Flexible Cables Follow text for justification / explanation • No resistance to bending (F always along cable) • Assumptions Horizontal component constant “Second order” terms drop out θ small, make use of trig. Identities • Find general relationship Differential equation Solve for y = f(x) Need know boundary conditions d y w = 2 dx T0 2 Case One - Parabolic Cable • Note Neglect weight of cable w is constant Useful for examining Suspension Bridges • Start by examine lowest point Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 293 Case One - Parabolic Cable wx 2 • Integrate => y = 2T0 • ... Lots of math and assumptions... • Equations for finding Tmax and cable length sA • Look at special case of hA = hB Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 293-295 Case Two - Catenary Cable • Weight of cable only load • Integration becomes much messier (hyperbolic functions) Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 295-296 Case Two - Catenary Cable • Difficult to solve analytically • Text suggest computational solution Catenary Cables won’t be on the Exam Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 296-297 Problem-Solving Approach • Unfortunately, a lot of equation-hunting Not as intuitive as other beams or fluids You won’t be required to memorize them • Identify the type of system • Remember where you “start” (where you set the origin of your coordinate system) Practice Problem 5/155 Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 300 Practice Problem 5/156 Meriam, JL and Kraige, LG. Statics 7th Ed. Wiley 2012. p. 300 For Next Class • Any Chapter 5 questions? • Read through Article 6/3 • Practice Problems 157, 161, 162