Learning Goal:To solve for the support reactions of a frame.The frame shown in (Figure 1) is supported by a pin at A and a pin at D. The two members are connected by a pin at C. Thedimensions are H₁ = 1.1 m, H₂ = 1.3 m, and L = 1 m. The applied force P = 11 kN acts at the midpoint of BC, and thedistributed load has intensity w = 1.3 kN/m.FigureH1BAPOWH₂<1 of 3>

Answered: Image /qna-images/answer/d1588126-e4bd-490f-a22e-e77063098190.jpg

Answered: Learning Goal: To solve for the support…

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.3.28P: A T-frame structure is torn posed of a prismatic beam ABC and a nonprismatic column DBF. The beam...

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A cable and pulley system in the figure part a supports a cage of a mass 300 kg at B. Assume that this includes the mass of the cables as well. The thickness or each of the three steel pulleys is t = 40 mm. The pin diameters are dPA= 25 mm, dB= 30 mm. and dc= 22 mm (see figure part a and part b). (a) Find expressions for the resultant forces acting on the pulleys at A, B. and C in terms of cubic tension T. (b) What is the maximum weight W that can be added to the cage at B based on the following allowable stresses? Shear stress in the pins is 50 MPa; bearing stress between the pin and the pulley is 110 MPa.
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.
A 150-lb rigid bar AB. with friction less rollers al each end. is held in the position shown in the figure by a continuous cable CAD. The cable is pinned at C and D and runs over a pulley at A. (a) Find reactions at supports A and B. (b) Find the force in the cable.
Repeat 1.3-9 but use the method of sections go find member forces in AC and BD.
A plane Frame is restrained at joints A and D, as shown in the figure. Members AB and BCD are pin connected at B. A triangularly distributed lateral load with peak intensity of SO N/m acts on CD. An inclined concentrated force of 200 N acts at the mid-span of BC. (a) Find reactions at supports A and D. (b) Find resultant forces in the pins at B and C.
A space truss has three-dimensional pin supports at joints 0, B, and C, Load P is applied at joint A and acts toward point Q. Coordinates of all joints arc given in feet (see figure). (a) Find reaction force components B x, B z, and Oz (b) Find the axial force in truss member AC.
The L-shaped arm ABCD shown in the figure lies in a vertical plane and pivots about a horizontal pin at A. The arm has a constant cross-sectional area and total weight W. A vertical spring of stiffness k supports the arm at point B. (a) Obtain a formula for the elongation of the spring due to the weight of the arm. (b) Repeat part (a) if the pin support at A is moved to D.
Beam AB has a pin support at A and a roller support at B Joint B is also restrained by a linearly elastic rotational spring with stiffness kR, which provides a resisting moment MBdue to rotation at B. Member AB has flexural rigidity EI. A moment M0acts counterclockwise at B. Use the method of superposition to solve for all reactions. Find an expression for joint rotation Ain terms of spring stiffness kR. What is Awhen kR 0? What is Awhen kR— ? What is Awhen kR= 6EI/L?
A plane frame has a pin support at A and roller supports at C and E (see figure). Frame segments A BD and CDEF are joined just left of joint 1) by a pin connection. (a) Find reactions at supports A. C. and E. (b) Find the resultant force in the pin just left of D.
Repeat Problem 2.5-9 for the flat bar shown in the figure but assume that and that
.15 A hitch-mounted bicycle rack is designed to carry up to four 30-lb bikes mounted on and strapped to two arms Gil (sec bike loads in the figure part a) The rack is attached to the vehicle at A and is assumed to be like a cant silkier beam A BCDGII (figure part b) The light of fixed segment AB is U = 10 lb. centered 9 in. from A (see figure part b) and the rest of the rack highs W2 = 40 lb. centered 19 in. from A. Segment ABCDG is a steel tube o(2 X 2 in. with a thickness I = 118 in. Segment BCDGII pivots about a bolt at B with a diameter d1 = 0.25 in. to allow access to the rear of the vehicle without removing the hitch rack. When in use, the rack is secured in an upright posit ion by a pin C(diameter o( pin d, = 5116 in.) (see phoo and figure part C). The of returning effect of the bikes on the rack is resisted by a force couple F h at BC. (a) Find the support reactions at A for the fully loaded rack. (b) Find forces in the bolt at B and the pin at C. (c) Find average shear stresses in both the bolt at Band the pin at C. (d) Find average bearing stresses o, in the bolt at B and the pin at C.
A framework ABC consists of two rigid bars AB and BC. Each having a length b (see the first part of the figure part a). The bars have pin connections at A, B, and C and are joined by a spring of stiffness k. The spring is attached at the midpoints of the bars. The framework has a pin support at A and a roller support al C, and the bars are at an angle a to the horizontal. When a vertical load P is applied at joint B (see the second part of the figure part a.) the roller support C moves to the right, the spring is stretched, and the angle of the bars decreases from a to the angle ??. (a) Determine the angle 0 and the increase S in the distance between points A and C. Also find reactions at A and C. (Use the following data: b = 200 mm. ft = 3.2 kN/m. a = 45°. and P = 50 N.) (b) Repeat part (a) if a translational spring kt= kll is added at C and a rotational spring kr= kb-l2 is added at A (see figure pan b).

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