EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 14, Problem 4P
(a) Start with an initial guess of
(b) Construct a plot from the results of (a) showing the path of the search.
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1. The truss shown is supported by hinge at A and cable at E.Given: H = 4m, S = 1.5 m, α = 75⁰, θ = 33⁰.Allowable tensile stress in cable = 64 MPa.Allowable compressive stress in all members = 120 MPaAllowable tensile stress in all members = 180 MPa1.Calculate the maximum permissible P, in kN, if the diameter of the cable is 20 mm.2.If P = 40 kN, calculate the required area (mm2) of member BC.3. If members have solid square section, with dimension 15 mm, calculate the maximum permissible P (kN) based on the allowable strength of member HI.ANSWERS: (1) 45.6 kN; (2) 83.71 mm2; (3) 171.76 kN
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2: A wire 4 meters long is stretched horizontally between points 4 meters apart. The wire is 25 mm2 in cross-section with a modulus of elasticity of 200 GPa. A load W placed at the center of the wire produces a sag Δ.1.Calculate the tension (N) in the wire if sag Δ = 30 mm.2.Calculate the magnitude of W, in N, if sag Δ = 54.3 mm.3. If W is 60 N, what is the sag (in mm)?ANSWERS: (1) 562 N, (2) 100 N, (3) 45.8 N
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4 : A cable and pulley system at D is used to bring a 230-kg pole (ACB) to a vertical position as shown. The cable has tensile force T and is attached at C. The length of the pole is 6.0 m, the outer diameter is d = 140 mm, and the wall thickness t = 12 mm. The pole pivots about a pin at A. The allowable shear stress in the pin is 60 MPa and the allowable bearing stress is 90 MPa. The diameter of the cable is 8 mm.1.Find the minimum diameter (mm) of the pin at A to support the weight of the pole in the position shown.2.Calculate the elongation (mm) of the cable CD.3.Calculate the vertical displacement of point C, in mm.ANSWERS: (1) 6 mm, (2) 1.186 mm, (3) 1.337 mm--
Chapter 14 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 14 - 14.1 Find the directional derivative of
at in...Ch. 14 - Repeat Example 14.2 for the following function at...Ch. 14 - 14.3 Given
Construct and solve a system of...Ch. 14 - (a) Start with an initial guess of x=1 and y=1 and...Ch. 14 - 14.5 Find the gradient vector and Hessian matrix...Ch. 14 - Prob. 6PCh. 14 - Perform one iteration of the steepest ascent...Ch. 14 - Perform one iteration of the optimal gradient...Ch. 14 - Develop a program using a programming or macro...Ch. 14 - 14.10 The grid search is another brute force...
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- A prototype automobile is designed to travel at 65 km/hr. A model of this design is tested in a wind tunnel with identical standard sea- level air properties at a 1:5 scale. The measured model drag is 529 N, enforcing dynamic similarity. Determine (a) the drag force on the prototype and (b) the power required to overcome this drag. See the equation Vm m = D V Dm (a) Dp = i (b) Pp = i N hparrow_forwardA new blimp will move at 6 m/s in 20°C air, and we want to predict the drag force. Using a 1: 14-scale model in water at 20°C and measuring a 2500-N drag force on the model, determine (a) the required water velocity, (b) the drag on the prototype blimp and, (c) the power that will be required to propel it through the air. (a) Vm = i (b) Dp = i (c) Pp = i m/s N Warrow_forwardDrag measurements were taken for a sphere, with a diameter of 5 cm, moving at 3.7 m/s in water at 20°C. The resulting drag on the sphere was 10 N. For a balloon with 1-m diameter rising in air with standard temperature and pressure, determine (a) the velocity if Reynolds number similarity is enforced and (b) the drag force if the drag coefficient in the equation below is the dependent pi term. li ε pVI D 1 = CD = Q μ (a) Vp = i (b) Dp = i m/s Narrow_forward
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