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(b) A beam element with four degrees of freedom is shown in Figure 1(b). The shape...
MEE456 Homework Consider the beam shown below: 550 Analyze this beam using a 3-node, 2-element model (hand calculations or E-200 G Pa and i=1 x 10" m'. Report on a summary page: a) Sketch a diagram of the beam showing the nodes, elements and loading (FE model). b) Present the displacements, rotations, reactions and, element forces and moments. c) Sketch a free body diagram of the beam showing the original loading and the reactions. d) Sketch a free body diagram...
For each beam shown in the associated figure, compute the deflection at the element nodes. The modulus of elasticity is E 10 x 10s psi and the cross section is as shown in each figure. Also compute the maximum bending stress. Use the finite element method with the minimum number of elements for each case.
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displacements, reactions and internal forces developed in the beam Note that there is a hinge at B. Take E = 250 GPa, 1-2000 cm 10 kN 2 kN/m 5 kN-m 10 m Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below....
Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam shown below. Form member and structure stiffness matrices and compute displacements, reactions and internal forces developed in the beam. Note that there is a hinge at B. Take E= 250 G Pa, 1 = 2000 cm- 10 kN 5 kN-m 2 kN/m 10 m Using the Stiffness Method procedure identify nodes, elements and degrees of freedom (neglect axial stiffness) for the beam...
Please not the same person any more 4 The figure below shows a 2D symmetric beam loaded as shown. Determine using the finite element method: a. The displacements at all nodes (both in translation and rotation), and b. If the distance from the centroid of the beam to its outside surface is 100 mm, determine the location of the point of highest and lowest stress in the beam. 8 KN -2 m- 5 E - 70 GPa 1 = 1...
Question2 A steel beam is designed to carry 2 umiform distributed loads which is shown in Figure e. Apply singularity function method and refer to the properties of the rolled-steed -W shape provided in the formula sheet, choose the most economical Wshape for the beam if the maximum allowable deflection at E is 5mm. Use E 200GPa. 119 marks! 115 kN/m 75 kN/m W - Shape Figure 02 Question2 A steel beam is designed to carry 2 umiform distributed loads...
finaite element 3. Consider the beam-bending problem shown below. Using one element and assuming that the beam length is , modulus of elasticity E, area A, and moment of inertial: a) Solve for unknown displacements. b) Find the displacement at x = 1/2 4. For problem 3 above assume that these is no truss axial effect or D.O.F Compute components of the element stiffness matrix using shape functions. K22 k23 k24 k33 k34 K44
Consider the beam shown in (Figure 1). E = 200 GPa and I = 62(106) mm 4 Figure 1 of 1 40 KN 18 kN.m Part A Determine the slope of the beam at B, measured counterclockwise from the positive x axis. Express your answer using three significant figures. V AED 11 vec t o Bera ? OB rad Submit Request Answer Part B Determine the deflection of the beam at C. Express your answer to three significant figures and...
For the beam elements shown (Node 1 is fixed and node 3 is a pin); the nodal displacements have been calculated in meters and radians as: V. V2 -0.001 V. 0.004 Let l 0.0001 m. and E 70 109 Nm: Neglecting the axial stiffness of the beam and using the interctions of a two-node beam element. (a) Find an equation for the slope of the beam in terms of the given nodal displacements and plot the slope diagram. (b) Find...
Consider the beam ABC of length L [m] in Figure 1 below, with simple supports at both ends. The beam supports a concentrated load P [N] at point B. You may assume the beam to be weightless in your analysis. Figure 1: Schematic of beam ABC. Part (a) Determine the vertical reaction forces at points A and C in terms of P. Part (b) Determine expressions (in terms of P and L) for the shear force, V(x) and the bending...