Castigliano's Theorem Calculate elongation of the rod under uniaxial loading
Problem 04.077- Determine the deflection of an angled bar using Castigliano's theorem Using Castigliano's theorem, determine the deflection of point B in the direction of the force F= 25 lbf for the steel bar shown in the figure where a = 15 in, b= 6 in, and the diameter is d= 0.625 in. The deflection of point B in the direction of force is
Derive an expression for the volume change of a bar subject to uniaxial loading in the x-direction. What is the volume strain for rubber?
. (20 points) Using Castigliano's theorem, determine the deflection of point B in the direction of the force F for the steel bar shown 207G po 168mm 12-mm dia. 168 mm o.8F 2. (20 points) The cantilevered handle in the figure is made from mild steel that has been welded at the Use Castigliano's theorem and F-=-600 N, Fu-800 N, and F,--400 N. . (20 points) Using Castigliano's theorem, determine the deflection of point B in the direction of the...
9. A smooth uniaxial rod with a cross-sectional area of 0.003 m² is made from a material with Sy = 300 MPa under R = -1 conditions, Su = 650 MPa, and of = 700 MPa. If the rod is subjected to a mean force of 180 kN, what is the allowable alternating force that will not cause failure in 106 cycles according to the Morrow criterion?
SOLVE B AND C USING CASTIGLIANO'S THEOREM Consider the cantilever beam shown in . Suppose that LAB = 640(106) mm IBC = 150(106) mm". Take E 200 GPa 12 kN/m 8 kN/m موا Inc Part A Part B Determine the displacement at point C measured downward. Use Castigliano's theorem. Express your answer to three significant figures and include the appropriate units. Enter positive value if the displacement is downward and negative value if the displacement is upward. HA ? Ac...
Use Castigliano's theorem to show that the maximum deflection for the end loaded cantilever beam as shown here is given by F13 3EI Neglect shear Ymax 3E 20
Member BC is joined to the horizontal beam by a pin at B. Use the Castigliano's 2nd Theorem and find the deflection at A and rotation at pin D 1. Members BC and DBA have the same A, E ahd I. 2.L 30° Member BC is joined to the horizontal beam by a pin at B. Use the Castigliano's 2nd Theorem and find the deflection at A and rotation at pin D 1. Members BC and DBA have the same...
Q1. A circular rod of 12 mm diameter was tested for tension. The total elongation on a 300 mm length was 0.22 mm under a tensile load of 17 KN. Find the value of E. (2.5 Marks) Answer: Q2. A prismatic bar has a cross section of 25 mm x 50 mm and a length of 2m under an axial force of 90 KN. The measured elongation of the bar is 1.5 mm. Compute the tensile stress and strain in...
3. Find the deflection at B by Castigliano's Second Theorem. Express your answer in terms of P and EI. (25 Points) 5P А C 21 B L/2 L/2
Q1. (45p) Use Castigliano's Theorem to find the vertical deflection at point B for the given member under the load of P. The member is fixed at A and free at the other end. 450 Divide the member in two sections AB and BC. Use the figures below if necessary BF a=45° Use the values below to compare the contribution of each component to total deflection. R = 75 mm, h = 30 mm, b = 15 mm. P =...