Using the theorem of Castigliano, find the horizontal (not vertical) deflection of the free end of the cantilever frame shown in the figure duc to the vertieal applied load P. Express your answers in terms of P, l (length), E (modulus of clasticity), A (cross sectional area) and I (moment of inertia of the cross section around the bending axis. Consider only bending and axial loading and assume that the cross-section is circular and that E, A, and I are constant.

Q: Q1) A cantilever beam of length L with uniform cross section is fixed as shown in figure. Determine…

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Q: For the beam and loading shown, use discontinuity functions to compute (a) the slope of the beam at…

A: From the given question it is required to calculate the slope of beam at B and deflection of beam at…

Q: Part A The simply supported shaft has a moment of inertia of 21 for region BC and a moment of…

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

A: ∑Ma=0⇒Cy*6-9*3*1.5=0                  ⇒Cy=6.75 KN∑Fy=0 ⇒Ay+Cy-9*3=0                 ⇒Ay=20.25 KN

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

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

A: Using double integration method

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

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Q: A horizontal simply-supported beam is loaded as shown in Figure 1. It has a rectangular cross…

A: h = 70 mm

Q: or the beam and loading shown, use discontinuity functions to compute (a) the slope of the beam at B…

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Q: For the cantilever beam shown, determine the (a) slope and (b) deflection at the free end B. El is…

A: Given:Required:Slope and displacement at free end B

Q: Find the deflection at the point of application of the load. The moment diagram for the load P is…

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Q: Q1) Determine the maximum deflection between the supports A and B. EI is constant. Use the method of…

A: Data given Find : Maximum deflection between supports A and B

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…

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Q: Find the slope deflections using any unit load method in the text book. For the beam shown in figure…

A: Strain Energy: The energy which is stored in any object loaded within the elastic elements is known…

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

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Q: For the beam and loading shown, use discontinuity functions to compute (a) the slope of the beam at…

A: Given:- Given Data:EI = 136000 kips.ft2w0=4.6kips/ft, LAB=13ft, LBC=7ft

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

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Q: 9. For the loading shown below, use the double-integration method to determine (a) the equation of…

A: Given data in question Cantilever beam Span LMoment at free end  MoTo find out Elastic…

Q: GPa, and I = 115 x 106 mm4 Answer:

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Q: A steel cantilever beam is of 1 m long, having a squa of 4 cm side length. The beam is fixed on one…

A: The given data is: Beam length, L=1 m Cross section=4 cm*4 cm E=210 GPa

Q: Using Conjugate-Beam Method, Determine the deflection at point C. EI = Constant; w=30kN/m; a=3m;…

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Q: 9. A clamped beam carries concentrated load P at the centre of span. Assume () 2nx w(x) = A 1- cos…

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

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

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Q: For

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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: The canitlevered beam is fixed on the left end and is subjected to the triangular distributed load…

A: Given information:Free body diagram is given below

Q: The beam supports the loads as shown in the figure. Using E= 200 GPa, w = 16KN/m, P= 16kN and M=…

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Q: Thumbs-up

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Q: Derive the maximum deflection using double integration method. simply supported beam with a…

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Q: Solve for the maximum deflection of the propped cantilever beam by the double integration method.…

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Q: Find the deflection at the point of application of the load. The moment diagram for the load P is…

A: Given:

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

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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: Using the theorem of Castigliano, find the HORIZONTAL deflection of the free end of the cantilever…

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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: 5. The rigid bar ABC shown in Figure, is hinged at A and supported by a steel rod at B. Determine…

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Q: Find the deflection at the point of application of the load. The moment diagram for the load P is…

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Q: Determine the internal moments at the supports of the beam shown.

A: MFCD = - 800 x 2 = - 1600 N-m

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

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

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Q: own, use the double-integration method to determine (a) the equation of the elastic curve for the…

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Q: For Beam AB (EI Constant), use the Unit Load Method to Determine: 1. The Deflection at C 2. The…

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Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.