Question 4Derive the equations of the deflection curve for a simple beam AB loaded by a couple(4 1)Mo acting at distance a from the left-hand support as shown in Figure Q4Determine the deflection , at the point where the load is applied Use the second-(4 2)order differental equation of the deflection curveMoAFigure Q4 Simply supported beam with a couple applied at its mid-span

Write the bending moment equation.

Answered: Question 4 Derive the equations of the…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A cantilever beam has a length L and is loaded by a triangularly distributed load of maximum intensity 9 at B. (Solve this problem by integrating the differential equations of the deflection curve. The beam has constant flexural rigidity EI.) RB = MA MA = RA Ⓡ Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B. (Use the statics sign convention. Use the following as necessary: 90, L.) RA = Need Help? 90 Read It B 000 Also solve for the equation of the deflection curve. (Enter the magnitude. Use the following as necessary: qo, L, E, I, x.) v(x) = Show My Work (Optional)? RB
For the loaded beam shown in the figure below: y 25 kN 20 kN 40 kN 1m 3 m 5 m Figure Q2: Loaded beam 2.1 Determine the reaction forces at the points of support of the beam shown in the figure Q2 above by applying the principle of equilibrium of moments. (Start your solution by drawing a free body diagram of the beam).
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Label the nodes and the elements in the figure with appropriate node and element numbers. Compute the local stiffness matrix and load vector for each element Assemble the global stiffness matrix and load vector. State the boundary conditions, apply them, and solve the reduced system to obtain the DOF solution Compute reactions at the supports Evaluate the deflection occurring at the midpoint of the 2nd portion of the beam (point C).
A propped cantilever beam is loaded by a bending moment of the magnitude M_B at the point B as shown in Figure Q1. The cross-section of the beam is a rectangle of the width w and the hight ℎ that are constant along the length of the beam L. The beam material’s Young’s modulus is Q. Assuming the positive deflections and positive vertical reaction forces are upward, calculate the value of the reaction forces at points A and B the absolute value of the reaction bending moment at point A A) Let R represent the reaction force at Support B. By releasing the beam at Support B and imposing a force R at Point B, the deflection of the beam consists of two parts,i.e. Part I- the deflection caused by M_B ; Part II- the deflection caused by R Please treat R, w, h , L , E as variables in this step , the mathematical equation for the deflection at Point B caused by R ( Part II) can be written as: b) Using the provided data: cross-section width w = 14 mm, cross-section hight h = 82…
Problem 1: (Please solve parts A and B of problem) A) A uniformly distributed load is subjected on the clamped-clamped beam and it is supported by a spring in the middle of the beam. Using Castigliano’s theorem, find the deflection in the spring. (Please use only Castigliano’s theorem to solve this part) B) Remove the spring in part A and use the Rayleigh-Ritz method to solve for the deflection at the middle of the beam. Assume that v(x) = C (1- Cos((2Pi*x)/L)) (Please use only Rayleigh-Ritz method for this part)
The beam is subjected to a point load and a distribution load as shown in Figure 3-1 below. (a) Find the reaction from supports B and E.(b) Draw a beam's Shear Force Diagram.(c) Draw the moment diagram of the beam.(d) If the cross-sectional area is shown in Figure 3-2, how many mm is the neural axis NA from the bottom? (e) Find the second moment of area, INA from the neural axis.(f) Find the maximum shear stress mmax from the beam.(g) Find the maximum tensile flexural stress mmax, T and maximum compressive flexural stress mmax, C on the beam, respectively.
For the loaded beam shown in Figure below : 2.1.Determine the reaction forces at the points of support of the beam in Figure Q2 above by applying the principle of equilibrium of moments and start your solution by drawing free body diagram of the beam. 2.2. Develop the equations for shear force and bending moment for the spans AB, BC and CD of the loaded beam shown above and for each equation developed, determine the values of shear forces and bending moment at the points A, B, C and D 2.3. Draw the shear force and bending moment diagrams for the loaded beam shown above.
5. A triangular plate cantilever beam represents an idealization of a leaf spring. Using Energy Methods, derive an expression for the deflection of the loaded end. b/2 b/2
For the beam and loading shown in Figure 5, determine the value of (r) at the point of action of the resuitant force of the distributed load using point B as the origin. Parabola Vertex 2000 N/m 900 N/m B 6 m A Figure 5: A parabolic distributed load on a beam AB. Answer: If the loading were analysed using point A as the origin, would the value of w at the location of the resultant change? Select one: a. No b. Yes
Pin-joint construction supports point loads as shown below: P Al ΕΙ C B 2/3 L 1/3 L a) Find the equation for the deflection of the bar at point B! b) Determine the equation for the moment that occurs at point A!
QUESTION 3 Given the beam shown in Figure Q3, calculate the reaction at point A, consider El to be constant. Wo Deformed Shape A B Figure Q3: Beam QUESTION 4 Determine the equivalent distributed load associated with the beam shown in Figure Q4. Determine the shear, moment, slope, and deflection equations, using the Macaulay functions and the singularity functions. 400N/m 20000NM 10m 5m 5m 2000N 2000N Figure Q4; Beam

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