EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 16, Problem 15P
A finite-element model of a cantilever beam subject to loading and moments (Fig. P16.15) is given by optimizing
where
FIGURE P16.15
A cantilever beam.
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A long steel rod is placed horizontally between two supports, one at each end. The rod bends a little in the center. Which property of this rod can be used to estimate how much the rod should bend at the center?
1.
Its Shear Modulus
2.
Its Young's Modulus
3.
All of these Moduli can be used to compute how much it bends.
4.
Its Bulk Modulus.
0.0062 0.0025 0.0012
Let D = 0.0025 0.0049 0.0025 be a flexibility matrix, with flexibility measured in inches per pound. Suppose that forces of 40, 10, and
0.0012 0.0025 0.0062
20 lb are applied to a beam at points 1, 2, and 3, respectively. Find the corresponding deflections y₁, y₂, and y3.
#1
#3
1
3₂
£₂
Y₁ = inch(es)
(Round to the nearest thousandth as needed.)
Y3
Q: Draw shear force and bending moment diagrams for the beam
shown below and then find max. shear force and bending
moment.
100 N
45
1.0
16 KN
1.2
1.7
1.9
Chapter 16 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
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equilibrium can be...
Ch. 16 - A chemical plant requires 106L/day of a solution....Ch. 16 - You must design a triangular open channel to carry...Ch. 16 - 16.13 As an agricultural engineer, you must design...Ch. 16 - 16.14 Find the optimal dimensions for a heated...Ch. 16 - A finite-element model of a cantilever beam...Ch. 16 - 16.16 Suppose that you are asked to design a...Ch. 16 - TheStreeter-Phelps model can be used to compute...Ch. 16 - Prob. 18PCh. 16 - 16.19 The flow in an open channel can be predicted...Ch. 16 - A cylindrical beam carries a compression load...Ch. 16 - The Splash River has a flow rate of 2106m3/d, of...Ch. 16 - 16.22 Determine the beam cross-sectional areas...Ch. 16 - AtotalchargeQ is uniformly distributed around a...Ch. 16 - A system consist softwopower plants that must...Ch. 16 - 16.25 The torque transmitted to an induction motor...Ch. 16 - (a) A computer equipment manufacture rproduces...Ch. 16 - A manufacturer provides specialized microchips....Ch. 16 - 16.28 The total drag on an airfoil can be...Ch. 16 - Mechanical/Aerospace Engineering
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- Q3. Fig Q3 shows a uniform cantilever beam of length L which is loaded by a linearly varying load: w(x) = wo where w is the load per unit length at the fixed end (x =0). L w(x) Fig Q3: A uniform cantilever beam (a) Using Ritz method, derive a two-term polynomial function to approximate the transverse displacement (u) of the beam. Total potential energy (TPE) for a beam under bending load is: TPE= EI d'u Jo 2 dx² -w(x)u dx where E is Young's modulus and I is second moment of area. (b) Calculate the bending moment at x = L based on Ritz solution.arrow_forwardA rectangular tube of outer width w = 7.5 m, outer height h = 5 m and thickness t = 0.17 m experiences bending through the x axis. What is the moment of inertia of the cross-sectional area In? y -- X MATLAB input variables: format shortEng W = 7.5; h = 5; t = 0.17; moment of inertia I, = m4arrow_forwardUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=3.5 ft, b=9.0 ft, c=4.0 ft, d=3.5 ft, w = 5.5 kips/ft and P = 45 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. For this loading, calculate the reaction forces Ay and Ey acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Ay =___________ kips, Ey = __________ kips. Determine the shear force acting at each of the following locations:(a) x = 0+ ft (i.e., just to the right of support A)(b) x = 3.5 ft(c) x = 12.5 ft(d) x = 16.5– ft (i.e., just to the left of D)(e) x = 16.5+ ft (i.e., just to the right of D)(f) x = 20.0– ft (i.e., just to the left of support E) Answer: a to f ) V = ________ kips Use the graphical…arrow_forward
- During a bicep curl on a bicep curl machine, I'm curling a weight stack of 100 pounds (single arm...I'm jacked like that). At this very moment, the weight stack has a moment arm of 0.12m, my elbow has an angle of 63deg, my muscle force vector has an angle of 23deg, and it attaches 3cm below my elbow joint on my radius. How much force must my bicep create right at this moment to hold the weight stack in place?arrow_forwardUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a= 3.5 ft, b= 8.0 ft, t, c= 5.0 ft, d= 3.0 ft, w = 8.5 kips/ft and P = 54 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. P В D E b d Calculate the maximum bending moment (i.e., either positive or negative) that occurs between points B and C. When entering your answers, use the bending moment sign convention. Answers: M = i kip-ft.arrow_forwardUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a= 3.5 ft, b= 8.0 ft, t, c= 5.0 ft, d= 3.0 ft, w = 8.5 kips/ft and P = 54 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. P В D E d The shear-force diagram crosses the V = 0 axis between points B and C. Determine the location x (measured from A) where V = 0 kips. Answer: x = i ft.arrow_forward
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