The beam shown below is supported by a pin at A and a roller at B and is a subjected to a 40kN load at L/2. Determine the deflection at C and the slope at A using: 1. The double integration method 2. The moment-area theorem 3. The conjugate beam method 4. Virtual work 5. Castigliano's theorem A L/2 40 KN L • C B

The beam shown below is supported by a pin at A and a roller at B and is a subjected to a 40kN load at L/2. Determine the deflection at C and the slope at A using: 1. The double integration method 2. The moment-area theorem 3. The conjugate beam method 4. Virtual work 5. Castigliano's theorem A L/2 40 KN L • C B

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

Q: The beam with, cross section shown, is subjected the load shown. Using E=200 GPa, determine the…

A: Maximum deflection occurs at the farthest point from the support. In spite of two support points, it…

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

A: Using double integration method

Q: A simple beam AB is subjected to a distributed load of intensity g(x) = sin -), where a, is the…

Q: L Mo

Q: 2. A simply supported beam carries a uniformly distributed load as shown below, determine the…

Q: 1. Draw the deflection diagram for the following figure 2. Use the double integration method to…

A: “Since you have asked solution with multiple method, we are solving with the double integration…

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: simply supported beam 10 m long carries a uniform load of 24 kN/m. Using E = 200 GPa, I = 240 x 10 6…

A: 62mm

Q: For the cantilever steel beam [E = 200 GPa; /= 135 × 106 mm4], use the double-integration method to…

Q: ANSWER: Mo A L B Determine the deflection and slope at point A using the method of integration. 1)…

A: Given data

Q: of How Walue of deflection at Points Card D by using doubl use EI=Snstant. loo KN

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: The magnitude of the concentrated load to be applied at the free end B of a cantilever beam as shown…

A: AB is a cantilever beam, where B is free end. Now, concentrated load is applied on free end i.e, B

Q: iniform simply supported beam, span Z, carries a distributed loading which varies according to a…

Q: Situation 3 Using double integration method, determine the slope and deflection at midspan of the…

A: E = 180 GPaI = 120 × 106 mm4Determine the slope and deflection at the mid span of the beam using…

Q: deflection at point B.

Q: Determine the slope and deflection at point 8 as shown in the beam using the three (3) methods…

A: Note: We’ll answer the first question since there are multiple questions specified. Please submit a…

Q: Remove the concentrated load Skips then compute the maximum slope and maximum deflection of the…

A: Given:- E=29000 ksi=4176000 kips/ft2I=76.8 in4=0.0037 ft2 To find:- Maximum slope and maximum…

Q: The beam is subjected to the linearly varying distributed load at segment AB and a uniformly…

A: The double integration method is solving the deflection and slope of a beam at any point. where x…

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

Q: Determine the slope at A and B and the deflection at C for

Q: I'm looking for: C. Conjugate Beam method

A: For using the conjugate beam method we should first draw the Bending moment(BM) diagram. Reaction at…

Q: Question 1 Specify the maximum deflection of the beam shown. El is constant. E = 200 GPa, I =…

Q: 1. Given is a 100 kN load acting at the midspan of a 6m. cantilever beam whose I = 5x10³ mm* and E =…

A: As you have asked different methods As per company's guidelines we can only answer first question.…

Q: 24KN/m 12KN/m Зт 5m Bm A simply supported beam is loaded as shown in the figure. Assume El is…

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

Q: W B X

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

A: (a) Vertical reaction at C = 30.55 kN (b) Moment at C = 66.78 kNm (c) Deflection at B = 6.78mm (d)…

Q: D. B F3m- -5 m

A: Given:- L=15m E=30GPa EI=constant I = 1800 x 106 mm4 To find:- The deflection at C

Q: using Double Integration Method, Determine the deflection at the free end of the beam shown

Q: A 10-m long simply supported beam carries a load that varies uniformly from zero at the left support…

Q: Please use CONJUGATE BEAM METHOD and show a complete and clear solution.

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Consider the cantilever beam in the figure, subject to a concentrated force P = 20kip at B and a…

Q: Part 2: for the frame shown below, P=20 kN and a=2 m, Assume I=20000 in and E=30,000 ksi for all…

A: Given:P = 20 kNa = 2mI = 20000 in4E = 30000 ksiRequired:Vertical deflection of E

Q: Determine the reaction forces at the end B of the beam shown in Figure Q6 by using the virtual-work…

A: Given Data:load=Wspan= LEI = Constant

Q: for the simply supported beam as shown below, assume El is constant and L is equal to 653. Using the…

Q: An overhanging beam is loaded as shown below. Calculate the deflections under the two loads 80kN and…

A: GIVEN DATA:-⇒Overhanging beam (single side) of span = 12 m⇒Loads = point loads:-(1) 80 KN(2) 120…

Q: a) Use the conjugate beam method to determine the slope and deflection of point A of the cantilever…

Q: 2. For a simply supported beam with a concentrated force, the coordinate system is selected as shown…

Q: Q3. a- A rectangular plate simply supported along its edges and subjected to a uniform of intensity…

A: "Since you have posted a question with multiple sub-parts, we will solve the first sub-part for you.…

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

The beam shown below is supported by a pin at A and a roller at B and is a subjected to a 40kN load at
L/2. Determine the deflection at C and the slope at A using:
1. The double integration method
2. The moment-area theorem
3. The conjugate beam method
4. Virtual work
5. Castigliano's theorem
A
L/2
40 kN
Į
• C
B

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 4 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

Problem 4: The beam is loaded as shown. Determine the slope and deflection at the midspan. Assume constant EI. Use P=1 (N) and M= 19 (N-m). Express your answers in terms of EI with appropriate units. Use the following methods: a. Double integration method b. Virtual work method P 1 m 2 m 1 m M R1 R2
SHOW COMPLETE AND CLEAN SOLUTION and DRAW ILLUSTRATION
Subject: Structural Theory 2 Task: Answer this question in different methods such as Double Integration method, area moment method, conjugate beam method, AND virtual work method.
SOLVE ONLY ONE OF THE FOLLOWING, using either the Unit Load Method/Method of Virtual Work or the Castigliano's Theorem: A A.) For the truss loaded as shown in Fig A, calculate the total deflection at joint D. Consider uniform cross sectional area A= 500mm² and modulus of elasticity E for all members is 200 GPa. B.) For the rigid frame shown in Fig B, calculate the horizontal deflection at point C. Members have the same moment of inertia of 1440 x 104 cm4 and E is constant at 210 GPa. P= 151 kN P in KN B H O G 4@3m 12 m Fig. A P in kN LL D 4m 120 kN/m B 120 kN/m A 4m Fig. B P in kN 3m 5m
A simply supported beam is 5m long and has a fixed support at the left-hand side and a roller support at the right-hand side, 2m from the roller support the beam is subjected to a 20KN point load. Determine the slope and deflection at the point load using Direct Integration Method. Take E = 2,1x10² GPa and I = 90x100 mm¹.
USE CONJUGATE BEAM METHOD IN SOLVING THE PROBLEM
Obtain the formula for the deformed beam shown below. Indicate the location of where the maximum deflection occurs and its value.Also obtain the deflection at point C and the rotation at point A for the beam using (a) the moment area method and (b) the conjugate method.
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 = 13 kN/m, L = 4.0 m, E = 205 GPa, and I = 105 x 106 mm4