Distributed loading on chapter 4 of the book entitled A First Course in the Finite Element Method. I would like to know how do they get the moment? Further more on example 4.3 equation 4.3.21. How to do we solve it simultaneously?
Distributed loading on chapter 4 of the book entitled A First Course in the Finite Element...
P=10 kN A cantilever beam is subiected to a concentrated force P, a uniformly distributed load w and a moment MI shown in the figure. Neglect the weight of the beam. (a) Draw the free body diagram for the beam showing all the 2 m reactions, replacing the support M.-2 kNm by the reaction forces/moments. (b) Use the equations of equilibrium to find the reaction forces/moments at R (c) Give the expression for the shear force, V- V(x), and the...
3. Analyze the system shown in Figure 3. (40 points) Copyright © McGraw-Hill Education. Permission required for reproduction or display 300 lb/ft - 4 ft 2 ft2 ft 300 lb Figure 2: Simply supported beam subject to a distributed load and a concentrated force Note: the Concentrated force at Point D induces a force on the beam and a moment on the beam both at Points C 3. Solve for the internal forces and moments in each region using integration...
QUESTION 1 [25 marks A frame loaded with a uniformly distributed load at Member AB and point load at Member BC and joint B. It has pinned supports A and C, while joint B is fixed connected, as can be seen in Figure 1. Take E-200 GPa. a) Using the slope-deflection method, calculate the moments and illustrate the bending moment diagram. [15 marks) b) Then calculate the shear forces and sketch the shear force diagram. [10 marks) 22 KN 10...
Problem 3 (19 points): A simply supported beam ABCD carries a uniformly distributed load, w, and a concentrated load, F, as shown in the figure. All the dimensions are given in the figure, and the weight of the beam is neglected a) Draw the free body diagram for the beam, showing all the applied and reaction forces. Find the reaction forces F=14 kN .6m b) Give the expression for the shear force, V- V(x), and the bending moment M M(x),...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the forces in each element. Then check equilibrium at node 4 Finally, draw the shear force and bending moment diagrams for each element. Let E 30x 103 ksi, A 8 in2, and I 800 in.4 for all elements. 20 kip 25 ft 25 ft 40 ft Figure P5-4...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the forces in each element. Then check equilibrium at node 4. Finally, draw the shear force and bending moment diagrams for each element. LetE 30 x 103 ksi, A = 8 in,2 , and 1-800 in.4 for all elements. 20 kip 25 ft 25 ft- 40 ft 20...
QUESTION 2 Beam ABCD is 8 m in length and is pin-supported at A and roller-supported at C as shown in Figure Q2. A counter-clockwise concentrated moment acts about the support A. A uniformly-distributed load acts on span BC and a vertical concentrated load acts at the free end D a) Determine the reactions at supports A and C. 4 marks) b) Obtain the shear force and the bending moment functions (in terms of x) for each segment along the...
Problem 2 Consider a simply supported symmetric I beam ABCD carrying a uniformly distributed load w and a concentrated load F as shown in Figure 2. Young's modulus of the beam is 200 GPa F- 8 kNN 8cm 3cm 3cm w- 6 kN/m 6cm 2cm Figure 2 1) Replace the support C with the reaction force Rc, and using static equilibrium find the reactions at point A and B in terms of Ro 2) Using the boundary conditions, calculate the...
Consider the frame in Fig. 1, the node and element numbers as well as the material and geometrical characteristics of the beam elements are also displayed on the same figure. The frame is subjected to two concentrated loads at nodes 2 and 3 and a uniform distributed load over beam 3. The frame is fixed at nodes 1 and 5. A global coordinate system is established with origin at node 1 and x-y axes positively directed to the right and...
8. The cantilever beam in Figure Q8 subjects to concentrated loading. The cross section geometry gives the second moment of area / 100 x 10 m. The longitudinal geometry of the beam: a 2 m, b 1 m. The material of the beam: Young's modulus E 200 GPa. The loading: concentrated force P 10 KN. (a) Determine the reactions to the beam at the fixed end. (b) Determine the rotation angle at point x-a (c) (Determine the deflection at the...