R1 1 m 40 kN 2 m 60 KN 3 m R2 a) A simply supported beam of length of 3 m has concentrated loads of 40 kN at 1 m from one end and 60 kN at 2 m from the same end as above figure. What is the deflection and slope of the beam at the 40 kN load? What is the maximum deflection and want position along the beam does it occur?. Suppose beam is Broad flange I beam which has section no of 400 and beam material is SAE 1010 steel. (You may review data table of the same to obtain design specifications)

R1 1 m 40 kN 2 m 60 KN 3 m R2 a) A simply supported beam of length of 3 m has concentrated loads of 40 kN at 1 m from one end and 60 kN at 2 m from the same end as above figure. What is the deflection and slope of the beam at the 40 kN load? What is the maximum deflection and want position along the beam does it occur?. Suppose beam is Broad flange I beam which has section no of 400 and beam material is SAE 1010 steel. (You may review data table of the same to obtain design specifications)

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.8.4P: A simple beam AB of length L is subjected to loads that produce a symmetric deflection curve with...

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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 q0= 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 of the height to the width of the cross section is (h:b) 2:1, Find the height h; and width h of the cross section of the beam.
A simple beam AB of length L is subjected to loads that produce a symmetric deflection curve with maximum deflection S 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 propped cantilever beam of length L = 54 in. with a sliding support supports a uniform load of intensity q (see figure). The beam is made of steel {<7y = 36 ksi) and has a rectangular cross section of width/) = 4.5 in. and height h = 6.0 in. What load intensity q will produce a fully plastic condition in the beam?
What is the span length L of a uniformly loaded, simple beam of wide-flange cross section (see figure) if the maximum bending stress is 12,000 psi, the maximum deflection is 0.1 in., the height of the beam is 12 in., and the modulus of elasticity is 30 × 106psi? (Use the formulas of Example 9-1.)
A simple beam of length L = 5 m carries a uniform load of intensity q = 5,8 kN/m and a concentrated load 22.5 kN (see figure). (a) Assuming tra]]ow = 110 MPa, calculate the required section modulus S. Then select the most economical wide-flange beam (W shape) from Table F-l(b) in Appendix F, and recalculate S, taking into account the weight of the beam. Select a new beam if necessary. (b) Repeat part (a), but now assume that the design requires that the W shape must be used in weak axis bending (i.e., it must bend about the 2-2 (or y) axis of the cross section).
The overhanging beam A BCD supports two concentrated loads P and Q (see figure), For what ratio PIQ will the deflection at point B be zero? For what ratio will the deflection at point D be zero? If Q is replaced by a uniform load with intensity q (on the overhang), repeat parts (a) and (b), but find ratio Pl(qa).
-6 Calculate the maximum deflection of a uniformly loaded simple beam if the span length L = 2.0 m, the intensity of the uniform load q = 2.0 kN/m, and the maximum bending stress = 60 MPa, The cross section of the beam is square, and the material is aluminum having modulus of elasticity E = 70 GPa. (Use the formulas of Example 9-1.)
A steel beam of rectangular cross section is 40 mm wide and 80 mm high (see figure). The yield stress of the steel is 210 MPa, (a) What percent of the cross-sectional area is occupied by the clastic core if the beam is subjected to a bending moment of 12.0 kN · m acting about the z axis? (b) What is the magnitude of the bending moment that will cause 50% of the cross section to yield?
Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses Jt(and k2^ and the beam has flexural rigidity EI. What is the downward displacement of point C, which is at the midpoint of the beam, when the moment MQis applied? Data for the structure are M0 = 7.5 kip-ft, L = 6 ft, EI = 520 kip-ft2, kx= 17 kip/ft, and As = 11 kip/ft. Repeat part (a), but remove Af0 and instead apply uniform load q over the entire beam.
A propped cantilever beam AB of length L and with a sliding support at A supports a uniform load of intensity q (see figure). Evaluate the strain energy of the beam from the bending moment in the beam. Evaluate the strain energy of the beam from the equation of the deflection curve.
A beam rests on supports at A and B and is loaded by a distributed load with intensity q as shown. A small gap exists between the unloaded beam and the support at C. Assume that span length L = 40 in. and flexural rigidity of the beam EI = 04 x 109lb-in2. Plot a graph of the bending moment at B as a function of the load intensity q. Hint: See Example 9-9 for guidance on computing the deflection at C.
A cantilever beam AB of length L = 6.5 ft supports a trapezoidal distributed load of peak intensity 4, and minimum intensity q/2tthat includes the weight of the beam (see figure). The beam is a steel W 12 × 14 wide-flange shape (see Table F-l(a), Appendix F). Calculate the maximum permissible load q based upon (a) an allowable bending stress eallow = 18 ksi and (b) an allowable shear stress eallow = 7,5 ksi. Note: Obtain the moment of inertia and section modulus of the beam from Table F-l(a).