Chapter 7, Problem 118P

Problem 4.30 While the stiffness of an elastic cord can be quite constant (i.e., the force versus displace- ment curve is a straight line) over a large range of stretch, as a bungee cord is stretched, it softens; that is, the cord tends to get less stiff as it gets longer. Assuming a soften- ing force-displacement relation of the form k8 - B83, where 8 (measured in ft) is the displacement of the cord from its unstretched length, considering a bungee cord whose unstretched length is 150 ft, and letting k = 2.58 lb/ft, determine the value of the con- stant B such that a bungee jumper weighing 170 lb and starting from rest gets to the bottom of a 400 ft tower with zero speed.

a machine mass m = 500 kg is mounted on a simply supported steel beam of length l = 2 that has a rectangular cross section (thickness = 0.1 m and width 1.2 m) and whose young modulus is given by E = 2.06x10 ^ 11 N / m2. To reduce the vertical deflection of the beam, a spring of stiffness k is added in the middle of the span, as shown in the following figure. Determine the value of k necessary to reduce the deflection of the beam by: a) -25% of its original valueb) -50% of its original valuec) -75% of its original value

P8.5 A beam is subjected to equal bending moments of M₂ = 45 kip-ft, as shown in Figure P8.5a. The cross-sectional dimensions (Figure P8.5b) are b₁ = 7.5 in., d₁ = 1.5 in., b2 = 0.75 in., d2 = 6.0 in., b3 = 3.0 in., and d3 = 2.0 in. Determine: (a) the centroid location, the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. State whether the normal stress at H is tension or compression. (c) the bending stress at point K. State whether the normal stress at K is tension or compression. (d) the maximum bending stress produced in the cross section. State whether the stress is tension or compression. K M₂ M₂ x H b₂ y b₁ b3 d₂ d

For a uniformly loaded span of a cantilever beam attached to a wall at x = 0 with the free end at x = L, the formula for the vertical displacement from y = 0 under the loaded condition with y the coordinate in the direction opposite that of the load can be written as follows: Y= -(X4 – 4X³ + 6X²) where Y is the vertical displacement, X = x/L, and L is the length of the beam. The formula was put into dimensionless form to answer the following question: What is the shape of the deflection curve when the beam is in its loaded condition and how does it compare with its unloaded perfectly horizontal orientation? The answer is provided graphically in Figure Q4. Figure Q4 shows the vertical deflection of a uniformly loaded cantilever beam and its comparison with the unloaded perfectly horizontal orientation. Write a script to get the same figure as Figure Q4 by solving the following question. 1 · Unloaded cantilever beam 0.5 Uniformly loaded beam -0.5 -1E > -1.5 -2- -2.5 -3 -3.5 0.5 1 1.5…

Part b) Bending moment by real forces_1 Let the origin of the horizontal coordinate x be at the support A and the positive x-axis points to the right. The bending moment caused by the real forces as a function of x can be discribed as For 0≤x≤9 m, (please use units kN.m for bending moment) (Use * for multiplication and ^ for exponentiation. For exmple, 2+² can be written as 2*x+x^2)

strength of materials

A composite beam is fabricated by bolting two 2.6-in.-wide by 13-in.-deep timber planks to the sides of a 0.6-in. by 13-in. steel plate. The moduli of elasticity of the timber and the steel are 1930 ksi and 31600 ksi, respectively. The simply supported beam spans a distance of 17 ft and carries two concentrated loads P, which are applied as shown. Assume Lag = LCD = 4 ft, Lgc = 9 ft, b = 2.6 in., d = 13 in. and t = 0.6 in. (a) Determine the maximum bending stresses o;, o, produced in the timber planks and the steel plate if P = 2.6 kips. (b) Assume that the allowable bending stresses of the timber and the steel are 1430 psi and 24200 psi, respectively. Determine the largest acceptable magnitude for concentrated loads P. (You may neglect the weight of the beam in your calculations.) P P B C D LAB LBC LCD d Cross scction Answers: ( a) σ, ksi, o, = i ksi. (b) P = i kips.

A composite beam is fabricated by bolting two 3.8-in.-wide by 13-in.-deep timber planks to the sides of a 0.7-in. by 13-in. steel plate. The moduli of elasticity of the timber and the steel are 1730 ksi and 30400 ksi, respectively. The simply supported beam spans a distance of 16 ft and carries two concentrated loads P, which are applied as shown. Assume LAB=LCD= 4 ft, Lgc = 8 ft, b = 3.8 in., d = 13 in. and t = 0.7 in. (a) Determine the maximum bending stresses 0, 0, produced in the timber planks and the steel plate if P = 2.7 kips. (b) Assume that the allowable bending stresses of the timber and the steel are 1430 psi and 18400 psi, respectively. Determine the largest acceptable magnitude for concentrated loads P. (You may neglect the weight of the beam in your calculations.) Answers: (a) o, = (b) P= LAB B LBC 4F Lodlod Cross section P kips. C ksi, 0, = LCD D ksi.

SITUATION 1: A T-beam is simply supported and is used to carry a uniform load of 20 kN/m. The beam is 4m long and has the following properties of 5 the T-beam are as follows: bf=500mm; tf=D100mm tw=200mm; dw3300mm PAV