2.99 See Answer

Question: A simple beam AB of length L

A simple beam AB of length L is subjected to loads that produce a symmetric deflection curve with maximum deflection δ at the midpoint of the span (see figure). How much strain energy U is stored in the beam if the deflection curve is (a) a parabola and (b) a half wave of a sine curve?
A simple beam AB of length L is subjected to loads that produce a symmetric deflection curve with maximum deflection δ at the midpoint of the span (see figure).
How much strain energy U is stored in the beam if the deflection curve is
(a) a parabola and
(b) a half wave of a sine curve?





Transcribed Image Text:

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> A cantilever beam is subjected to a quadratic distributed load q(x) over the length of the beam (see figure). Find an expression for moment M in terms of the peak distributed load intensity qo so that the deflection is δB = 0. q(x) = qo

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> A cantilever beam is subjected to load P at mid-span and counterclockwise moment M at B (see figure). (a) Find an expression for moment M in terms of the load P so that the reaction moment MA at A is equal to zero. (b) Find an expression for moment M in

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> A cantilever beam AB of length L = 6 ft is constructed of a W8 × 21 wide-flange section (see figure). A weight W = 1500 lb falls through a height h = 0.25 in onto the end of the beam. Calculate the maximum deflection δmax of the

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> Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses k1 and k2 and the beam has flexural rigidity EI. (a) What is the downward displacement of point C, which is at the midpoint of the beam, when the moment Mo is applied?

> The cantilever beam AB shown in the figure has an extension BCD attached to its free end. A force P acts at the end of the extension. (a) Find the ratio a/L so that the vertical deflection of point B will be zero. (b) Find the ratio a/L so that the angle

> A simple beam AB supports five equally spaced loads P (see figure). (a) Determine the deflection δ1 at the midpoint of the beam. (b) If the same total load (5P) is distributed as a uniform load on the beam, what is the deflection Î&acu

> A cantilever beam AB carries three equally spaced concentrated loads, as shown in the figure. Obtain formulas for the angle of rotation θB and deflection δB at the free end of the beam. L L 3

> A cantilever beam carries a trapezoidal distributed load (see figure). Let wB = 2.5 kN/m, wA = 5.0 kN/m, and L = 2.5 m. The beam has a modulus E = 45 GPa and a rectangular cross section with width b = 200 mm and depth h = 300 mm. WA WB B LA L h

> A cantilever beam of a length L = 2.5 ft has a rectangular cross section (b = 4 in, h = 8 in) and modulus E = 10,000 ksi. The beam is subjected to a linearly varying distributed load with a peak intensity qo = 900 lb/ft. go A. B L

> Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of superposition, calculate the deflection at joint C. Assume that L = 4 m, a = 2 m, q = 15 kN/m , P = 7.5 kN , E = 200 GPa, and I = 70.8 × 106 mm4. C

> Copper beam AB has circular cross section with a radius of 0.25 in. and length L = 3 ft. The beam is subjected to a uniformly distributed load w = 3.5 lb/ft. Calculate the required load P at joint B so that the total deflection at joint B is zero. Assume

> An object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). The beam has a rectangular cross section of area A. Assuming that h is very large compared to the deflection of the beam when the weight W is applied sta

> A simply supported beam (E = 1 2 GPa) carries a uniformly distributed load q = 125 N/m, and a point load P = 200 N at mid-span. The beam has a rectangular cross section (b = 75 mm, h = 200 mm) and a length of 3.6 m. Calculate the maximum deflection of th

> A simple beam AB is subjected to couples Mo and 2Mo acting as shown in the figure. Determine the angles of rotation θ A and θ B at the ends of the beam and the deflection δ at point D where the load Mo is applied.

> The simple beam AB shown in the figure supports two equal concentrated loads P: one acting downward and the other upward. Determine the angle of rotation θA at the left hand end, the deflection δ1 under the downward load, and th

> A simple beam AB is subjected to a load in the form of a couple Mo acting at end B (see figure). Determine the angles of rotation θA and θB at the supports and the deflection δ at the midpoint. Mo A B L

> A simple beam AB supports two concentrated loads P at the positions shown in the figure. A support C at the midpoint of the beam is positioned at distance d below the beam before the loads are applied. Assuming that d = 10 mm, L = 6 m, E = 200 GPa, and I

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> Calculate the deflections δB and δC at points B and C, respectively, of the cantilever beam ACB shown in the figure. Assume Mo = 36 kip-in, P = 3.8 kips, L = 8 ft, and EI = 2.25 × 109 lb-in2. Mo

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> A simple beam ACB supporting a uniform load q over the first half of the beam and a couple of moment Mo at end B is shown in the figure. Determine the strain energy U stored in the beam due to the load q and the couple Mo acting simultaneously. Mo A

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> An overhanging beam ABC rests on a simple support at A and a spring support at B (see figure). A concentrated load P acts at the end of the overhang. Span AB has length L, the overhang has length a, and the spring has stiffness k. Determine the downward

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> The frame ABC supports a concentrated load P at point C (see figure). Members AB and BC have lengths h and b, respectively. Determine the vertical deflection δC and angle of rotation θC at end C of the frame. (Obtain the solutio

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> A cantilever beam ACB supports two concentrated loads P1 and P2, as shown in the figure. Determine the deflections δC and δB at points C and B, respectively. (Obtain the solution by using the modified form of Castiglianoâ&

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> A simple beam AB of length L and height h undergoes a temperature change such that the bottom of the beam is at temperature T2 and the top of the beam is at temperature T1 (see figure). Determine the equation of the deflection curve of the beam, the angl

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> A simple beam AB of length L is loaded at the left-hand end by a couple of moment Mo (see figure). Determine the angle of rotation θA at support A. (Obtain the solution by determining the strain energy of the beam and then using Castigliano&

> A uniformly loaded simple beam AB (see figure) of a span length L and a rectangular cross section (b = width, h = height) has a maximum bending stress σmax due to the uniform load q. Determine the strain energy U stored in the beam. A B L

> The cantilever beam ACB shown in the figure has moments of inertia I2 and I1 in parts AC and CB, respectively. (a) Using the method of superposition, determine the deflection δB at the free end due to the load P. (b) Determine the ratio r of

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> A simply supported beam (E = 1600 ksi) is loaded by a triangular distributed load from A to C (see figure). The load has a peak intensity qo = 10 lb/ft, and the deflection is known to be 0.01 in. at point C. The length of the beam is 12 ft, and the ratio

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> The cantilever beam shown in the figure supports a triangularly distributed load of maximum intensity qo. Determine the deflection δB at the free end B. (Obtain the solution by determining the strain energy of the beam and then using Castigl

> A simply supported beam is loaded with a point load, as shown in the figure. The beam is a steel wide flange shape (W 12 × 35) in strong axis bending. Calculate the maximum deflection of the beam and the rotation at joint A if L = 10 ft, a =

> The beam shown in the figure has a sliding support at A and a roller support at B. The sliding support permits vertical movement but no rotation. Derive the equation of the deflection curve and determine the deflection δA at end A and also &

> Derive the equations of the deflection curve for a simple beam AB with a distributed load of peak intensity qo acting over the left-hand half of the span (see figure). Also, determine the deflection δC at the midpoint of the beam. Use the se

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> Derive the equations of the deflection curve for a cantilever beam AB carrying a uniform load of intensity q over part of the span (see figure). Also, determine the deflection δB at the end of the beam. Use the second-order differential equa

> Derive the equations of the deflection curve for a simple beam AB loaded by a couple Mo acting at distance a from the left-hand support (see figure). Also, determine the deflection δo at the point where the load is applied. Use the second-or

> The beam shown in the figure has a sliding support at A and a spring support at B. The sliding support permits vertical movement but no rotation. Derive the equation of the deflection curve and determine the deflection δB at end B due to the

> A simple beam with an overhang is subjected to a point load P = 6 kN. If the maximum allowable deflection at point C is 0.5 mm, select the lightest W360 section that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the b

> A cantilever beam has a length L = 12 ft and a rectangular cross section (b = 16 in, h = 24 in). A linearly varying distributed load with peak intensity qo acts on the beam. (a) Find peak intensity qo if the deflection at joint B is known to be 0.18 in.

> A cantilever beam AB supporting a triangularly distributed load of maximum intensity qo is shown in the figure. Derive the equation of the deflection curve and then obtain formulas for the deflection dB and angle of rotation θB at the free e

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> Beams AB and CDE are connected using rigid link DB with hinges (or moment releases) at ends D and B (see figure a). Beam AB is fixed at joint A and beam CDE is pin-supported at joint E. Load P = 150 lb is applied at C. (a) Calculate the deflections of jo

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> A two-span, continuous wood girder (E = 1700 ksi) supports a roof patio structure (figure part a). A uniform load of intensity q acts on the girder, and each span is of length 8 ft. The girder is made up using two 2 × 8 wood members (see fig

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2.99

See Answer