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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1. A spring mass system serving as a shock absorber under a car's suspension, supports the M=1000kgmass of the car. For this shock absorber,k=1000N/m and c=2000N s/m. The car drives over a corrugated road with force F=2000sin(wt)N. Use your notes to model the second order differential equation suited to thisapplication. Simplify the equation with the coefficient of x'' as one. Solve x (the general solution) interms of using the complimentary and particular solution method. In determining the coefficients ofyour particular solution, it will be required that you assume w2 -1=w or . Do not 1-w2=-wuse Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.You must indicate in your solution:1. The simplified differential equation in terms of the displacement x you will be solving2. The m equation and complimentary solution3. The choice for the particular solution and the actual particular solution xp4. Express the solution x as a piecewise…
2- Derive the rule-of-mixtures expression for the composite extensional modulus E₁ assuming the existence of an interphase region. The starting point for the derivation would be the model shown below. For simplicity, assume the interphase, like the matrix, is isotropic with modulus E¹. With an interphase region there is a volume fraction associated with the interphase (i.e.,V;). For this situation: vf + vm + vi = 1 H |w²||wm|
mhm 4.31 System for Exercise 4.24 (left) and Exercise 4.25 (right). m, the force required to deflect the end, as is illustrated in Figure 4.32 is In Chapter 11 we are much smarter and are able to show that for a cantilever ЗЕЛ L3 X, 4.32 Cantilever beam subjected to a at the end. F = ere E is the modulus of elasticity, which is a property of the material used, I is area moment of inertia of the cross-section of the beam, and L is the length. If a mass m,is attached to the end of the beam, what is the equation of motion the vertical motion of the beam? If the length is doubled, what is the change in quency of the free vibration of the beam? =kX 2 Guieds x=0 F-XX F x = L Fig. 4.33 Rotatin 4.28. Referring the end of a ca elasticity of the length is L = 1 1. Determine t 2. Determine t @= 1000 r 4.29. Determin 1. On the sam 2. Identify the the part you
For point a, suggest different form but same equation.
For point a, suggest a different form but the same equation without removing u
Deflections after the partial UDL on cantilever beam formula. Here are the inputs: Span: 205mm, UDL: 2 N/mm, UDL start: 100mm, UDL length: 100mm, Point of interest: 205mm, Elastic modulus: 210000N/mm2, Second moment of area: 4218.75 mm4
A square domain is modeled using either one bilinear rectangular element or two linear triangular elements as shown below. a) Determine the system element matrix for the Laplace equation for each discretization. b) Determine the displacement at the center of the domain (0.5,0.5) in terms of the nodal displacement. Hint: You need to assemble the stiffness matrix for the system on the right to form a 4*4 matrix from the two 3*3 element matrices. 1.0 4. 1.0 3. X- 1.0 1.0 2. 2.
For the cantilever steel beam [E = 180 GPa; / = 102 x 106 mm4], use the double- integration method to determine the deflection vg at B. Assume L = 3.8 m, Mo = 68 kN-m, and w = 17 kN/m. Answer: VB i mm. W Save for Later L eTextbook and Media Attempto unlimit Mo
%3! Q4: - For static system as shown in figure below, if k 50 N/mm, m =m2, u = 0.25 for the blocks m, and m2, tensions TI= 28.35N, spring elongation 5 mm and the force F1 m, cos 0 + m, sin 0. Find the inclination angle, Tension in other wire, and the mass of blocks. By using the Grammar method. T2 m2 T1 ml F1
Finite Element Method It is made of steel material (210GPa) for the beam given below, beam cross section (dimensions mm) is given below. According to this a) Find the displacement that occurs at each node b) Find the reaction forces

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