Q3. Fig Q3 shows a uniform cantilever beam of length L which is loadedby a linearly varying load:w(x) = wowhere w is the load per unit length at the fixed end (x =0).Lw(x)Fig Q3: A uniform cantilever beam(a) Using Ritz method, derive a two-term polynomial function toapproximate the transverse displacement (u) of the beam.Total potential energy (TPE) for a beam under bending load is:TPE=EI d'uJo 2 dx²-w(x)u dxwhere E is Young's modulus and I is second moment of area.(b) Calculate the bending moment at x = L based on Ritz solution.

Beam Deflection using Ritz Method (Two-Term Polynomial)Given:A cantilever beam of length L.Young's…

Answered: Q3. Fig Q3 shows a uniform cantilever…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Problem 4Given: The cylindrical piling for an offshore platform is expected to encounter currents of 160 cm/s and waves of a 12 s period and 3 m height.Required: If a 1:60 scale model is tested in the wave tank, what will be the current speed
A cantilever beam (with a clamp at x=0 and free at x=L, where L is the length of the beam) is modelled using two flexural elements. A moment, M, is applied at the free end. Which of the following describes the vector of external forces? Note that no other external forces are applied, and the degrees of freedom are defined in the usual order. f = [0 0 0 0 M 0]T f = [0 0 M 0]T f = [0 0 0 0 0 M]T f = [0 0 0 M]T f = [M 0 0 0]T f = [0 M 0 0]T
A Rayleigh’s method approximation for the first flexural natural frequency of a beam that is simply supported at both ends was using the guessed shape lx^2-x^3. How many of the boundary conditions are satisfied with this guess?
A hydraulic line with a closed end has the following parameters. L = 3 m, D = 10 mm, p = 867 kg/m³ ,u = 0.13 Ns/m² and B = 1 GPa. Calculate the coefficients of the transfer function.
(VI.) In the following figure, a uniform beam of length 6.00 meters is supported by a horizontal cable and a hinge at angle 60.0 degrees, the weight of the beam and the box are 4.00x10^2 and 1.00x10^3 N respectively. Find out a) the tension in the cable, b) the forces the hinge exerts on the beam.
Find the axial displacement of a rod given properties L(length), A (cross sectional area), E (Modulus) impacted axially by a mass m moving with a velocity v0?
Suppose a spring with spring constant k=1 supports a mass of 1kg and is subject to a driving force f(t)=sin2t. The mass is initially at rest at its equilibrium point. At time t=2, the mass is hit with a sharp upward blow, so that the force of the blow is δ(t−2). Set up and solve (using Laplace transforms) an initial-value problem modelling this situation.
A beam, uniform in mass, M = 47.6 kg and length L = 10.2 m, hangs by a cable supported at point B, and rotates without friction around point A. On the end far of the beam, an object of mass m = 24.3 kg is hanging. The beam is making an angle of θ = 30.9° at point A with respect to the + x-axis. The cable makes an angle φ = 21.1° with respect to the - x-axis at B. Assume ψ = θ + φ. a. Enter an expression for the lever arm for the weight of the beam, lB, about the point A. b. Find an expression for the lever arm for the weight of the mass, lm. c. Write an expression for the magnitude of the torque about point A created by the tension T. Give your answer in terms of the tension T and the other given parameters and trigonometric functions. d. Enter an expression the horizontal component of the force, Sx, that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables available in the palette. e. Enter an expression for the vertical component of…
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the location of the maximum deflection, and (c) the maximum beam deflection. Assume that EI is constant for the beam. Let w = 12 kN/m, L = 6.0 m, E = 215 GPa, and I = 105 x 106 mm4.
A uniform aluminum beam 9.00 m long, weighing 300 N,rests symmetrically on two supports 5.00 m apart (Fig. ). A boyweighing 600 N starts at point A and walks toward the right. (a) In thesame diagram construct two graphs showing the upward forces FA andFB exerted on the beam at points A and B, as functions of the coordinatex of the boy. Let 1 cm = 100 N vertically and 1 cm = 1.00 m horizontally.(b) From your diagram, how far beyond point B can the boy walkbefore the beam tips? (c) How far from the right end of the beam shouldsupport B be placed so that the boy can walk just to the end of the beamwithout causing it to tip?
Consider an electrical motor with mass M= 29 kg located at the tip of a rigid beam pivoted at point A, with the other end supported by a spring and damper with stiffness, k = 6 MN/m and damper c= 12 kNs/m, as shown in the figure below. Assume that the rigid beam is massless, the length is L= 1.3 m (horizontal distance between point O and pivot point A), and zero initial conditions. If there is an unbalanced mass of m0=2 kg in the rotating part of the motor, eccentricity is e =382 mm, and the rotor is rotating with a speed of w (omega) = 203 rad/s, determine the maximum amplitude response of point O at steady state condition in millimetre. Assume the line of actions of forces created by spring and damper act through point O, the centre of electric motor. Treat the electric motor mass as a point mass for calculating its moment of inertia about point A.
Consider the following linear equations,

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