Answered: By the concept of Fourier series, write…

By the concept of Fourier series, write expression for qo deflection as function of (x) for simply supported beam shown in Figure. Then find the deflection at mid-span and rotation at first end.

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: .6-1 A cantilever beam AB is subjected to a uni- orm load of intensity q acting throughout its…

A: Given that:

Q: 4. The cantilever beam AB is of uniform cross section and its load is shown in figure 4. El for beam…

Q: Describe how to use the virtual work principle to find the horizontal displacement at D in the…

A: Length of member AB = 2L Length of member BC = L Length of member CD = L Flexural rigidity, EI is…

Q: A -3 m B -3 m IC + -3 m- 60 kN m

Q: A beam is shown in the figure below, and the flexural stiffness of the beam section is constant El:…

A: As bot mention which method to used for finding deflection at point C . Let's solve using…

Q: Use the Moment-area Method to obtain the Slope of Point A after deformation and the vertical…

A: Given- A beam having flexural stiffness of the beam section EI constant. Required- to Use the…

Q: 10 kips 3 kips/ft D B. 3 ft 4 ft 3 ft

Q: A cantilever beam carries an uniform load w along its entire length, L. EI is constant. a) Calculate…

Q: A 4-meter cantilever beam supports a uniformly distributed load of w=25 kN/m at half of its span;…

A: Determinea. Deflection at the free end in terms of E. b. Slope at the free end in terms of E.

Q: Q4\ Use the Finite Difference Method to determine the deflections at the nodes of the simply…

Q: -2 m -4 m- C 4 m

Q: A uniform horizontal beam is simply supported at it's left end x=0 but fixed at the other end X=L as…

A: A propped cantibeam is given with hinged end support.

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

H.W
By the concept of Fourier series, write expression for qo
deflection as function of (x) for simply supported beam
shown in Figure. Then find the deflection at mid-span
and rotation at first end.
9⁰ 9(x)
ㅏ
1 1-x
9(x) = 90(1-
90(1-x)_90²-90x
90x
L
= 9

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 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

Use the method of virtual work, for example, virtual integration, and principle of superposition , handwritten work only don’t forget FBDs and ensure neatness pls.
Consider the cantilever beam in the figure. Knowingthat a = 6m, and that P = 18kN, use the moment areamethod to calculate the following:(a) The slope of point C(b) The deflection of point B
a = 15m w = 24knm E=200GPA I = 70x10^6 Explain how you would determine the deflection at c using double integration method. Write down relevant equations but no need to simplify or solve them
Answer 2a please
3) The T shaped cross-section of a beam is made of a flange (the upper horizontal area A1 = 2000 mm2) and a web (the lower vertical area A2 = 3200 mm?) as shown in the figure. 20 mm If you want to compute the vertical distance C, of the centroid of this cross-section from the bottom most point of this cross- а. section then give the expression in terms of some numbers from which Cy can be computed. No need to carry out the calculation. b. From part (a) if you get Cy = 114.6 mm then give the final expression of the area moment of inertia Ix (about the x-axis going through the centroid of the T-section). Your expression should only contain some numbers. No need to finish the calculation. Give the final expression of the area moment of inertia ly (about the y-axis going through the centroid). Your expression should only contain some numbers. No need to finish the calculation. d. If you drill a circular hole of 15 mm diameter with its center 160 mm С. 20 mm 100 mm coinciding with the…
2. P Derive an equation that describes the vertical deflection of the beam, y(x), and also B calculate the maximum deflection of the beam. M = 0.5PL %3D
Loads PA and PB are applied to a uniform cantilever beam AC, causing deflections SA and dB at A and B, respectively. Using the second- order integration method, determine expressions for PA and PB in terms of E, I, L, SA, and SB.
Here is the follow up,
A cantilever beam AB is loaded as shown in Figure 1. EI is constant for the beam. L = 2.7 m and P = 8.9 kN. Write down your L and P values and answer parts a to c below. (a) Using the moment area method, determine the slope of the beam at B. (b) Using the conjugate beam method, determine vertical deflection at B. (c) Draw the free body diagram (FBD) of the virtual force system for the virtual work method to determine the vertical deflection at the mid-span of the beam. (Note: No calculations are required and show only the FBD).
Compute the vertical and horizontal component of the deflection at C of the frame in the following figure using the method of virtual force. The direction of uniformly distributed loading is "→". Take E=200GPa, I=240(106)mm4.
Rigid bar ABC is supported by bronze rod (1) and stainless steel rod (2) as shown in the figure. A concentrated load of P = 16 kips is applied to the free end of bronze rod (3). Determine the magnitude of the deflection of rod end D after the temperature of all rods has increased by 125°F. Use the following dimensions and properties: a = 2.8 ft, b = 6.3 ft. Rod (1): d₁ = 0.90 in., L₁ = 11 ft, E₁ = 15,200 ksi, α₁ = 12.20 × 10-6/°F. Rod (2): d₂ = 0.80 in., L₂ = 9 ft, E2 = 28,000 ksi, a₂ = 9.60 × 10-6/F. Rod (3): d3 = 1.25 in., L3 = 5 ft, E3 = 15,200 ksi, a3 = 12.20 x 10-6/°F. VD = i L in. (1) A a L3 B (3) D b Rigid bar L2
Problem 3 Conjugate Beam Method: For the given beam below, answer the questions. El = constant: P M=Pa B a a (a) Draw the conjugate beam (clearly show the supports of the conjugate beam and mark the important values). (b) Determine the slope angle at point B, 0B, of the real beam using the conjugate beam method. Determine the deflection at point B, Ag, of the real beam using the conjugate beam method.