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