An elevated jogging track is supported at intervals by a wood beam AB (L = 7.5 ft) that is pinned at A and supported by steel rod BC and a steel washer at B. Both the rod (d B C = 3/16 in.) and the washer (d B = 1.0 in.) were designed using a rod tension force of T B C =415 lb. The rod was sized using a factor of safely of 3 against reaching the ultimate stress tr u — 60 ksi. An allowable bearing stress s b a = 565 psi was used to size the washer at B. A small platform HF is suspended below a section of the elevated track to support some mechanical and electrical equipment. The equipment load is uniform load q = 50 lb/ft and concentrated load W E = 175 lb at mid-span of beam HF. The plan is to drill a hole through beam ABaX £land install the same rod (d B C ) and washer) d B ) at both D and F to support beam HF. (a) Use s and to check the proposed design for rod DF and washer d,: are they acceptable? (b) Re-check the normal tensile stress in rod BC and bearing stress at 8 if either is inadequate under the additional load from platform HF. Re-design them to meet the original design criteria.
An elevated jogging track is supported at intervals by a wood beam AB (L = 7.5 ft) that is pinned at A and supported by steel rod BC and a steel washer at B. Both the rod (d B C = 3/16 in.) and the washer (d B = 1.0 in.) were designed using a rod tension force of T B C =415 lb. The rod was sized using a factor of safely of 3 against reaching the ultimate stress tr u — 60 ksi. An allowable bearing stress s b a = 565 psi was used to size the washer at B. A small platform HF is suspended below a section of the elevated track to support some mechanical and electrical equipment. The equipment load is uniform load q = 50 lb/ft and concentrated load W E = 175 lb at mid-span of beam HF. The plan is to drill a hole through beam ABaX £land install the same rod (d B C ) and washer) d B ) at both D and F to support beam HF. (a) Use s and to check the proposed design for rod DF and washer d,: are they acceptable? (b) Re-check the normal tensile stress in rod BC and bearing stress at 8 if either is inadequate under the additional load from platform HF. Re-design them to meet the original design criteria.
Solution Summary: The author evaluates the proposed design for rod DF and washer F.
An elevated jogging track is supported at intervals by a wood beam AB (L = 7.5 ft) that is pinned at A and supported by steel rod BC and a steel washer at B. Both the rod (dBC= 3/16 in.) and the washer (dB= 1.0 in.) were designed using a rod tension force of TBC=415 lb. The rod was sized using a factor of safely of 3 against reaching the ultimate stress tru— 60 ksi. An allowable bearing stress sba= 565 psi was used to size the washer at B.
A small platform HF is suspended below a section of the elevated track to support some mechanical and electrical equipment. The equipment load is uniform load q = 50 lb/ft and concentrated load WE= 175 lb at mid-span of beam HF. The plan is to drill a hole through beam ABaX £land install the same rod (dBC) and washer) dB) at both D and F to support beam HF.
(a) Use s and to check the proposed design for rod DF and washer d,: are they acceptable?
(b) Re-check the normal tensile stress in rod BC and bearing stress at 8 if either is inadequate under the additional load from platform HF. Re-design them to meet the original design criteria.
Branch of science that deals with the stationary and moving bodies under the influence of forces.
Spur gears
Note : Exam is open notes &tables / Answer all questions.
Q.1. The press shown for Figure.1 has a rated load
of 22 kN. The twin screws have double start Acme
threads, a diameter of 50 mm, and a pitch of 6 mm.
Coefficients of friction are 0.05 for the threads and
0.08 for the collar bearings. Collar diameters are 90
mm. The gears have an efficiency of 95 percent and a
speed ratio of 60:1. A slip clutch, on the motor shaft,
prevents overloading. The full-load motor speed is
1720 rev/min.
(a) When the motor is turned on, how fast will the
press head move? (Vm= , Vser. =
)
(5M)
(b) What should be the horsepower rating of the
motor? (TR=, Tc= Pser. =
"
Bronze
bushings
Foot
Motor
Bearings
watt, Pm= watt, Pm= h.p.) (20M)
2['s
Fig.1
Worm
Collar
bearing
Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 1 Solutions
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
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BEARINGS BASICS and Bearing Life for Mechanical Design in 10 Minutes!; Author: Less Boring Lectures;https://www.youtube.com/watch?v=aU4CVZo3wgk;License: Standard Youtube License