A simply supported beam of a total length ll is shown in Figure Q5, where point A is supported by a pin connection and point C is supported by a roller support. The concentrated load is P=mgP=mg at the location of l1l1. Note that l1/l=l1/l= 0.65. Determine the shear-force and bending-moment distributions produced in the beam by the concentrated load PP. A simply supported beam of a total length l is shown in Figure Q5, where point A issupported by a pin connection and point Cis supported by a roller support. Theconcentrated load is P = mg at the location of l1. Note that 4/l = 0.65. Determine theshear-force and bending-moment distributions produced in the beam by theconcentrated load P.Note that adatpive marking has been used to consider the method mark.myFigure Q5: A simply supported beam with a concentrated load applied a)(1) The support reaction forces at the A and C, in terms of P,be careful of the sign.R(mathematical expression)R(mathematical expression)(2) Give the expressions of the shear and moment at an arbitrary poistion z of ABsegment, in terms of P and a, be careful of the sign.(mathematical expression)M2(mathematical expression)(3) Give the expressions of the shear and moment at an arbitrary poistion z of BCsegment, in terms of P and æ, be careful of the sign.V =(mathematical expression)М, —(mathematical expression)

f a total length ll is shown in Figure Q5, where point A is supported by a pin connection and point C is supported by a roller support. The concentrated load is P=mgP=mg at the location of l1l1. Note that l1/l=l1/l= 0.65. Determi

f a total length ll is shown in Figure Q5, where point A is supported by a pin connection and point C is supported by a roller support. The concentrated load is P=mgP=mg at the location of l1l1. Note that l1/l=l1/l= 0.65. Determi

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter10: Statically Indeterminate Beams

Section: Chapter Questions

Problem 10.3.14P: A propped cantilever beam of a length L is loaded by a concentrated moment M0at midpoint C Use the...

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-4-13 A propped cantilever beam of a length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic spring with stiffness k. Use the method of superposition to solve for all reactions. Also draw shear-force and bending-moment diagrams, labeling all critical ordinates. Let k = 6EI/L3.
A cantilever beam of a length L and loaded by a uniform load of intensity q has a fixed support at A and spring support at B with rotational stiffness kR. A rotation B at B results in a reaction moment MB=kRxB. Find rotation B and displacement Bat end B. Use the second-order differential equation of the deflection curve to solve for displacements at end B.
A propped cantilever beam of a length L is loaded by a concentrated moment M0at midpoint C Use the second-order differential equation of the deflection curve to solve for reactions at A and B. Draw shear-force and bending-moment diagrams for the entire beam. Also find the equations of the deflection curves for both halves of the beam, and draw the deflection curve for the entire beam.
Repeat Problem 6.4-14 but use the configuration of channel shapes and loading shown in the figure. Use P = 250 N.
A thin steel beam AB used in conjunction with an electromagnet in a high-energy physics experiment is securely bolted to rigid supports (see figure), A magnetic field produced by coils C results in a force acting on the beam. The force is trapezoidally distributed with maximum intensity q0= 18 kN/m. The length of the beam between supports is L = 200 mm, and the dimension c of the trapezoidal load is 50 mm. The beam has a rectangular cross section with width b = 60 and height h = 20 mm. Determine the maximum bending stress max and the maximum deflection for the beam. (Disregard any effects of axial deformations and consider only the effects of bending. Use E = 200 GPa.)
A counterclockwise moment M0acts at the midpoint of a fixed-end beam ACB of length L (see figure). Beginning with the second-order differential equation of the deflection curve (the bendingmoment equation), determine all reactions of the beam and obtain the equation of the deflection curve for the left-hand half of the beam. Then construct the shear-force and bending-moment diagrams for the entire beam, labeling all critical ordinales. Also, draw the deflection curve for the entire beam.
A fixed-end beam AB of a length L is subjected to a uniform load of intensity q acting over the middle region of the beam (sec figure). Obtain a formula for the fixed-end moments MAand MBin terms of the load q, the length L, and the length h of the loaded part of the beam. Plot a graph of the fixed-end moment MAversus the length b of the loaded part of the beam. For convenience, plot the graph in the following nondimensional form: MAqL2/l2versusbL with the ratio b/L varying between its extreme values of 0 and 1. (c) For the special case in which ù = h = L/3, draw the shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.
A propped cantilever beam of a length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic rotational spring with stiffness kR,which provides a resisting moment MBdue to rotation B . Use the method of superposition to solve for all reactions. Also draw shear-force and bending-moment diagrams, labeling all critical ordinates. Let kR= El/L.
A beam ABCD with a vertical arm CE is supported as a simple beam at .1 and D (see figure). A cable passes over a small pulley that is attached to the arm at E. One end of the cable is attached to the beam at point B. The tensile force in the cable is 1800 lb. Draw the shear-Force and bending-moment diagrams for beam A BCD. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations. Repeat part (a) if a roller support is added at C and a shear release is inserted just left of C (see figure part b).
B cams 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\ Calculate the deflections of joints B and joint C Assume L = 9 ft and EI = 127,000 kip-in2. Repeat part (a) if rigid link DB is replaced by a linear spring with k = 20 kips/in (see figure b).
Repeat 1.3-9 but use the method of sections go find member forces in AC and BD.
A foot bridge on a hiking trail is constructed using two timber logs each having a diameter d = 0.5 m (see figure a). The bridge is simply supported and has a length L = 4 m. The top of each log is trimmed to form the walking surface (see Fig, b)LA simplified model of the bridge is shown in Fig. g. Each log must carry its own weight w = 1.2 kN/m and the weight (P = 850 N) of a person at mid-span, (see Fig. b). Determine the maximum tensile and compressive stresses in the beam (Fig, b) due to bending. If load h is unchanged, find the maximum permissible value of load ... if the allowable normal stress in tension and compression is 2.5 M Pa.