Using Castigliano’s Theorem, compute the value of the following for the beam shown:(a) Slope at point A(b) Vertical displacement of point C 3. Using Castigliano's Theorem, compute the value of the following for the beamshown:(a) Slope at point A(b) Vertical displacement of point C5000 N4.5 kN.m"A1.5 m1.5 m3.20 kN/m3 mB1....1.5 mC

Answered: Using Castigliano's Theorem, compute…

Using Castigliano's Theorem, compute the value of the following for the beam shown: (a) Slope at point A (b) Vertical displacement of point C 4.5 kN.m A 1.5 m 5000 N 1.5 m 3.20 kN/m 3m B 1.5 m C

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: Problem 2: For the beam shown, compute 1. the deflection midway between supports 2. the deflection…

A: Given AB= 1 m , BC= 3 m , CD= 2m , DE= 2 m

Q: Draw the deflection diagram of the beam. Then using the double integration method, derive the…

Q: Draw the approximate deflected shape from the bending moment diagram. Develop the piecewise…

Q: The timber beam in Figure 2 is simply supported at points A and E. The cross-section of the beam…

Q: Using double integration method, determine the maximum deflection in the following beam and the…

Q: The cantilever beam loaded as shown has the following properties: El = constant. Using Double…

A: Using double integration method

Q: 1. A beam has a simple span of 7.0 m it is subjected to a concentrated load of 30 kN and 75 kN at a…

Q: A 12 foot cantilever beam has a fixed support at point A and is subjected to a distributed load of 2…

Q: For the beam and loading shown, use the double-integration method to determine (a) the equation of…

Q: L Mo

Q: Consider that a box section is used for the beam loaded as shown in figure. Using flexure and shear…

A: Given: A hollow square cross-section Required : Moment of inertia about centroidal x axis

Q: Determine the following unknowns on the beam shown below using Double Integration Method. Consider…

A: Given Data:Section 150×150mmE=200Gpaa=5mb=11kN/mc=3kNd=7kN/mTo determine:Deflection at point B in…

Q: tion of the maximum deflection, and (c) the maximum beam deflection. Assu = 4.0 m, E = 200 GPa, and…

Q: 1800Nm f+ zm. 200N/m 2m/+2m 2m 2m +++2m

A: As per company's guidelines we can only answer first question Kindly post other questions as…

Q: For the given beam below, the 8 KN load is changed to 93 KN and the 4 KN load is also changed to 12…

A: Given data 8 KN load changed to 93 KN and 4 KN load also changed to 12 KN Find C1 value in KNm2…

Q: A simply supported beam 10 m long carries a uniform load of 24 kN/m. Using E = 200 GPa, I = 240 x…

Q: er beam o- (F), as sl са

A: Let us consider a section as shown below from the free end. For moment equilibrium, Mx=-wx22…

Q: Compute the slope at point A and deflection at point C of the beam in evious problem using…

Q: 2. A simply supported beam of length L carries a point load P in the downward direction at its…

A: To find the deflection at the mid point. Using 4th order differential equation Virtual work method…

Q: • Determine the SLOPE AND DISPLACEMENT at point A. TAKE E = I1 GPA. THE VALUE OF "I" CAN BE SOLVED…

Q: Problem 3. Determine the following unknowns on the beam shown below using Conjugate-Beam Method.…

Q: Using Double Integration Method, determine the equation of the elastic curve of the beam below and…

Q: For the beam and loading shown, use the double-integration method to determine (a) the equation of…

Q: r the beam and loading shown, use the double-integration method to determine (a) the equation of the…

A: To find maximum deflection and it's location

Q: For the beam and loading shown, use the double-integration method to determine (a) the equation of…

A: Given Data:W=kN/mL=4.5mE=180GpaI=110×106mm4 It is required to calculate deflection at free end, at B…

Q: For the simply supported displacements at E and C. values along the member

Q: For the beam and loading shown, use the double-integration method to determine (a) the equation of…

Q: GPa, and I = 115 x 106 mm4 Answer:

Q: The simply supported steel beam is loaded by the 20 kN - m couple as shown in the figure. Using E =…

A: Given:- To find:- Using the double integration method, it is required to calculate the displacement…

Q: 2. A simply supported beam is loaded as shown in the figure. Using Castigliano's Theorem determine…

Q: A 60 kN/m 2.0 m OB 120 kN.m 3.0 m 30 kN C 3.0 m D

A: Find the slope and deflection using double integration method.

Q: For the beam and loading shown, use the double-integration method to determine (a) the equation of…

A: Given data: w = 14 kN/m, L = 4.5 m, E = 215 GPa, and I = 125 x 106 mm4 It is asked to determine…

Q: simply supported beam is loaded as shown in the figure. Assume EI is constant. Using Castigliano’s…

Q: Answer: (b)x= (c) Vmax = L E mm Wo B X

Q: m, L = 5.5 m, E = 205 GPa, and I= 140 x 10° mm. L wer: m max= mm I3D

Q: 2. A simply supported beam is loaded as shown in the figure. Using Moment-Area Method determine the…

Q: For the beam and loading shown, use the double-integration method to determine (a) the equation of…

A: Hi! Thank you for the question, as per the honor code, we are allowed to answer three sub-parts at a…

Q: For the beam and loading shown, use the double-integration method to determine (a) the equation of…

A: Given data w = 11 KN/m L = 5m E = 200 GPA = 2 × 105 N/mm2 I = 115 × 106 mm4

Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

Using Castigliano’s Theorem, compute the value of the following for the beam shown:
(a) Slope at point A
(b) Vertical displacement of point C

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: State the given data

VIEW

Step 2: Support reaction for slope calculation at A

VIEW

Step 3: Integration of moment and derivatives

VIEW

Step 4: Support reaction for deflection calculation at C

VIEW

Step 5: Integration of moment and derivatives

VIEW

Solution

VIEW

Step by step

Solved in 6 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

A simply supported beam carries a uniformly distributed load as shown below, determine the deflection and slope develop at point B. Use Conjugate Method
Double Integration The given overhanging beam is loaded as shown. Use E = 1.5 x 10^6 psi and I = 40 in^4. A) determine the deflection at point B in inches. B) determine the location of the maximum deflection from the left support in ft. C) determine the maximum deflection in inches and calculate the slope of elastic curve over the right support.
From the given beam loaded as shown, Let P = 12 kips, L = 6 ft, a = 3 ft. E = 29 x 10^6 psi, I = 722 in^4. use double integration method a. Equation of the slope b. Equation of the deflection curve c. Position of the maximum deflection at segment AB from point A d. Maximum deflection.
GIVEN: The simply supported beam shown below is homogeneous, prismatic and has point forces F, applied as shown. E=constant L=constant F, ↑ F, L{2 L{2 REQUIRED: 1) Using beam theory, derive an expression for each of the following: a) V, =V,(x, p,L) b) M. = M¸(x, p,L) c) o =0-(x, y, p,I_,L,E) d) E = E„(x,y, p,,I,L,E) y y %3D XX e) v, =v,(x, p,I_,L,E) Vo
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, and (b) the deflection at B. Assume that El is constant for the beam. Let w = 15 kN/m, L = 3.5 m, E = 190 GPa, and I = 120 x 106 mm4 W B ·4/27 Answer: (b) VB = ·L/27 mm
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the location of the maximum deflection, and (c) the maximum beam deflection. Assume that El is constant for the beam. Let w = 9 kN/m, L = 3.0 m, E = 195 GPa, and I = 150 x 10° mm“. B Answer: (b) x = (c) Vmax = mm
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the slope at A, (c) the slope at B, and (d) the deflection at midspan. Assume that EI is constant for the beam. Let M0 = 55 kN·m, L = 6.0 m, E = 215 GPa, and I = 110 x 106 mm4.
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, and (b) the deflection at B. Assume that EI is constant for the beam. Let w = 12 kN/m, L = 5.5 m, E = 215 GPa, and I = 120 x 106 mm4
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the maximum deflection, and (c) the slope at A. Assume that El is constant for the beam. Let w = 14 kN/m, L = 4.0 m, E = 215 GPa, and I = 110 x 106 mm4. B Answer: (b) Vmax = i mm (c) OA - i rad
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the location of the maximum deflection, and (c) the maximum beam deflection. Assume that El is constant for the beam. Let w = 12 kN/m, L = 3.0 m, E = 215 GPa, and I = 130 x 106 mm4. Wo B Answer: (b) x = (c) Vmax = mm
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the slope at A, (c) the slope at B, and (d) the deflection at midspan. Assume that EI is constant for the beam. Let M0 = 45 kN·m, L = 4.5 m, E = 220 GPa, and I = 145 x 106 mm4. Draw a free body diagram of the beam and solve the reaction forces Ay and By. The diagram shows these forces in their positive directions. Your answers may be negative.
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the maximum deflection, and (c) the slope at A. Assume that El is constant for the beam. Let w = 11 kN/m, L= 3.0 m, E = 185 GPa, and I = 120 x 106 mm4. Answer: (b) Vmax = i mm (с) Өд — і rad