@ The beam is loaded by its self-weight with intensity q. The length of the beam is 11.2 ft. Let E= 30,000 ksi. (Integrate the differential equation of the deflection curve. The beam has constant flexural rigidity EI.) (a) Calculate the reactions at joints A and B. (Assume the positive vertical direction is upward and the positive direction for moments is counterclockwise. Use the statics sign convention. Enter your forces in lb and your moment in lb-ft.) RA = lb RB = lb MA = lb-ft (b) Find the location of zero moment (other than at B) within span AB. (Enter your answer in feet. Assume x = 0 is at A and the +x-axis increases to the right.) x = ft (c) Calculate the maximum deflection of the beam (in inches) and the rotation at joint B (in radians). (Enter the magnitudes.) 8max = in. 8B = rad

@ The beam is loaded by its self-weight with intensity q. The length of the beam is 11.2 ft. Let E= 30,000 ksi. (Integrate the differential equation of the deflection curve. The beam has constant flexural rigidity EI.) (a) Calculate the reactions at joints A and B. (Assume the positive vertical direction is upward and the positive direction for moments is counterclockwise. Use the statics sign convention. Enter your forces in lb and your moment in lb-ft.) RA = lb RB = lb MA = lb-ft (b) Find the location of zero moment (other than at B) within span AB. (Enter your answer in feet. Assume x = 0 is at A and the +x-axis increases to the right.) x = ft (c) Calculate the maximum deflection of the beam (in inches) and the rotation at joint B (in radians). (Enter the magnitudes.) 8max = in. 8B = rad

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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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

100%

A propped cantilever steel beam is constructed from a W12 x 35 section.
A
9
The beam is loaded by its self-weight with intensity q. The length of the beam is 11.2 ft. Let E = 30,000 ksi. (Integrate the differential equation of the deflection curve. The beam has constant flexural rigidity EI.)
(a) Calculate the reactions at joints A and B. (Assume the positive vertical direction is upward and the positive direction for moments is counterclockwise. Use the statics sign convention. Enter your forces in lb and your moment in lb-ft.)
RA =
lb
lb
RB =
MA =
lb-ft
x =
(b) Find the location of zero moment (other than at B) within span AB. (Enter your answer in feet. Assume x = 0 is at A and the +x-axis increases to the right.)
ft
(c) Calculate the maximum deflection of the beam (in inches) and the rotation at joint B (in radians). (Enter the magnitudes.)
8max =
in.
8 B =
rad

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3. A T-shaped structure is acted in by a distributed load that varies from 100 N/m to 0 N/m and by a force P. Attached at A and C are two cables. Each of the cables is attached to a ring at E. A 600 N weight is suspended from the ring. The structure can rotate about B but is held in the position shown by the force P. a. From the geometry of the problem, determine the distance d, b. If the total moment about B is equal to zero, what is the magnitude of force P, and c. Determine the tensions in cables EA and EC. B 100 N/m 0.825 A 1.50- P 78° -0.625 260 E 600 N
SOLVE USING THREE MOMENT EQUATION
For the beam and loading shown, EI is constant. Note that the beam is statically indeterminate to the first degree. (a) Determine the equations of the elastic curve for the beam using the x coordinate. (b) Determine the slope at A. A L- wo B
Calculate the reactions at the supports of the following statically indeterminate beam, using the Method of Cross and applying the simplifications. Consider that the supports A and D are hinges and the supports B and C are rollers. Consider that EI is constant:
1. A 200mm x 300mm beam has a simple span of 8 meters. It is necessary to place a support at midspan because of the excessive deflection at the center in order to limit the deflection to 12mm and such that the moment at that point is zero. E = 13,800 MPa. a. Determine the load carried by the beam. Express your answer in N/m. b. Compute for the reaction at the support at midspan so that the beam will not deflect at its midpan. c. Find the bending stress of the beam so that it will not deflect at its midspan. W- N/m 4m Pz 200 mm RI 300mm
SOLVE BY STRICTLY CONJUGATE BEAM METHOD