Two beams (ABCD and DE) are connected using a pin at Point D. The pin acts as a moment release,i.e. no moments are transferred through this pinned connection. Shear forces can be transferredthrough the pinned connection at point D. Beam ABCD has a pinned support at point A and a rollersupport at Point C. Beam DE has a roller support at Point E. A concentrated load, P, is applied to themid span of beam DE, as shown below. Another concentrated load, 2P, is applied to Point G. Thebracket BFG can be considered rigid.A oG2P|

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Answered: Two beams (ABCD and DE) are connected…

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 10.4.17P: Beam ABC is fixed at support A and rests (at point B) upon the midpoint of beam DE (see part a of...

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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.
Segments A B and BCD of beam A BCD are pin connected at x = 4 m. The beam is supported by a sliding support at A and roller supports at C and D (see figure). A triangularly distributed load with peak intensity of SO N/m acts on EC. A concentrated moment is applied at joint D. (a) Find reactions at supports A, C, and D. (b) Find internal stress resultants N, Y, and Mat x = 5m. (c) Repeat parts (a) and (b) for die case of the roller support at C replaced by a linear spring of stiffness kr™ 200 kN/m (see figure).
A square wood platform is 8 ft × 8 ft in area and rests on masonry walls (see figure). The deck of the platform is constructed of 2-in. nominal thickness tongue-and-groove planks (actual thickness 1.5 in.; sec Appendix CL) supported on two S-ft long beams. The beams have 4 in. × (i in. nominal dimensions (actual dimensions 3.5 in. × 5.5 in.). The planks arc designed to support a uniformly distributed load n ( lb/ft" i acting over the entire top surface of the platform. I be allowable bending stress for the planks is 2400 psi and the allowable shear stress is 100 psi. W ben analyzing the planks, disregard their weights and assume that their reactions are uniformly distributed over the top surfaces of the supporting beams. (a) Determine the allowable platform load Mr. (lb/ft2) based upon the bending stress in the planks. (b) Determine the allowable platform load if-. (lb/ft-) based upon the shear stress in the planks. (c) Which of the preceding values becomes the allowable load alolow on the platform? Hints: Use care in constructing the loading diagram for the planks, noting especially that the reactions are distributed loads instead of concentrated loads. Also, note that the maximum shear forces occur at the inside faces of the supporting beams.
Segments AB and BCD of beam ABCD are pin connected at x = 10 ft. The beam is supported by a pin support at A and roller supports at C and D; the roller at D is rotated by 30* from the x axis (see figure). A trapezoidal distributed load on BC varies in intensity from 5 lb/ft at B to 2.5 lb/ft at C. A concentrated moment is applied at joint A, and a 40-lb inclined load is applied at the mid-span or CD. (a) Find reactions at supports A, C, and D. (b) Find the resultant force in the pin connection at B. (c) Repeat parts (a) and (b) if a rotational spring(kr= 50 ft-lb/radian ) is added at A and the roller at C is removed.
-4-4 A cantilever beam is supported at B by cable BC. The beam carries a uniform load q = 200 N/M. If the length of the beam is L = 3 m, find the force in the cable and the reactions at A. Ignore the axial flexibility of the cable.
Beam ABC is fixed at support A and rests (at point B) upon the midpoint of beam DE (see part a of the figure). Thus, beam, ABC may be represented as a propped cantilever beam with an overhang BC and a linearly elastic support of stiffness k at point B (see part b of the figure). The distance from A to B is L = 10 ft, the distance from B to C is L/2 = 5 ft, and the length of beam DE is L = 10 ft. Both beams have the same flexural rigidity EI. A concentrated load P = 1700 lb acts at t lie free end of beam ABC. Determine the reactions RA, RB+ and MAfor beam ABC. Also, draw the shear-force and bending-moment diagrams for beam ABC, labeling all critical ordinates.
An L-shaped reinforced concrete slab 12 Ft X 12 ft, with a 6 Ft X 6 ft cut-out and thickness t = 9.0 in, is lifted by three cables attached at O, B, and D, as shown in the figure. The cables are are combined at point Q, which is 7.0 Ft above the top of the slab and directly above the center of mass at C. Each cable has an effective cross-sectional area of Ae= 0.12 in2. (a) Find the tensile force Tr(i = 1, 2, 3) in each cable due to the weight W of the concrete slab (ignore weight of cables). (b) Find the average stress ov in each cable. (See Table I-1 in Appendix I for the weight density of reinforced concrete.) (c) Add cable AQ so that OQA is one continuous cable, with each segment having Force T, which is connected to cables BQ and DQ at point Q. Repeat parts (a) and (b). Hini: There are now three Forced equilibrium equations and one constrain equation, T1= T4.
Continuous cable A DB runs over a small friction less pulley al D to support beam OABC, which is part of an entrance canopy for a building (see figure}. The canopy segment has a weight W = 1700 lb that acts as a concentrated load in the middle of segment AB. (a) What is the maximum permissible value of load P at C if the allowable force in the cable is 4200 lb? (b) If P = 2300 lb, what is the required diameter of pins A, B, and D? Assume that the pins are in double shear and the allowable shear stress in the pins is 10 ksi.
Cantilever beam AB carries an upward uniform load of intensity q1from x = 0 to L/2 (see Fig. a) and a downward uniform load of intensity q from x = L/2 to L. Find q1in terms of q if the resulting moment at A is zero. Draw V and M diagrams for the case of both q and qtas applied loadings. Repeat part (a) for the case of an upward triangularly distributed load with peak intensity q0(see Fig. b). For part (b), find q0, instead of q1
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.
Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1or L2) and outer diameters (d1or different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load q = 2PIL is applied over a distance of 3L/4 along BC, and concentrated load PIA is applied downward at D. (a) Derive a formula for the displacement
Continuous cable ADB runs over a small friction less pulley at D to support beam OABC, which is pan of an entrance canopy for a building (see figure). A downward distributed load with peak intensity q0= 5 kNVm al O acts on the beam (see figure). Assume that canopy weight W = S kN and that the cable cross-sectional area is 100 mm". What is the required diameter of pins A, B. and D if the pins are in double shear and the allowable shear stress is SO MPa? Note that dimensions OA = AB = BC = 1.5 m.

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