2. Two rollers of the same diameter shown in the figure are supported by an inclined plane and a vertical wall. If all surfaces are smooth, find the reactions induced at points A, B, and C. ( 120N 80N B 30
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A: Using the equilibrium equation tanθ=0.40.3θ=53.13° ∑Fx=0RAH+RDH=500 ....(1)∑Fy=0RAV+RDV=0…
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Q: 2니3 니3
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Q: Answer the attached file
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Q: L
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A: ∵ΣMA=0 →NB x 0.75 = 60 x 1 →NB= 80N
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A: Free Body Diagram
Two rollers of the same diameter
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- 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.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.The fixed-end bar ABCD consists of three prismatic segments, as shown in the figure. The end segments have a cross-sectional area A1= 840 mm2and length Lt= 200 mm. The middle segment has a cross-sectional area A2= 1260 mm2 and length L2= 250 mm. Loads PBand Pcare equal to 25.5 kN and 17.0 kN, respectively. (a) Determine the reactions RAand RDat the fixed supports. (b) Determine the compressive axial force FBCin the middle segment of the bar.
- Find support reactions at 4 and Band then use the method of joints to find all member forces. Let b = 3 m and P = 80 kN.A circular bar ACB of a diameter d having a cylindrical hole of length .r and diameter till from A to C is held between rigid supports at A and B. A load P acts at U2from ends A and B. Assume E is constant. (a) Obtain formulas for the reactions R, and RBat supports A and B. respectively, due to the load P (see figure part a). (b) Obtain a formula for the displacement S at the point of load application (see figure part a). (c) For what value of x is RB= (6/5)?,? (See figure part a.) (d) Repeat part (a) if the bar is now rotated to a vertical position, load P is removed, and the bar is hanging under its own weight (assume mass density = p). (See figure part b.) Assume that x = LI2.A lube structure is acted on by loads at B and D, as shown in the figure. The tubes are joined using two flange plates at C that are boiled together using six 0.5-in. diameter bolts. (a) Derive formulas for the reactions RAand REat the ends of the bar. (b) Determine the axial displacements S£. Sc, and SDat points B, C. and D. respectively. (c) Draw an axial-displacement diagram (ADD) in which the abscissa is the distance x From support A to any point on the bar and the ordinate is the horizontal displacement Sat that point. (d) Find the maximum value of the load variable P if allowable normal stress in the bolts is 14 ksi.
- By what distance h does the cage shown in the figure move downward when the weight W is placed inside it? (See the figure.) Consider only the effects of the stretching of the cable, which has axial rigidity EA = 10,700 kN. The pulley at A has a diameter da= 300 mm and the pulley at B has a diameter dB= 150 mm. Also, the distance L1= 4.6 m, the distance L2=10.5 m, and the weight W = 22 kN. Note: When calculating the length of the cable. include the parts of the cable that go around the pulley sat A and B.A crane boom of mass 450 leg with its center of mass at C is stabilized by two cables AQ and BQ (Ae= 304 mm2 for each cable) as shown in the figure. A load P = 20 KN is supported at point D. The crane boom lies in the y-z plane. (a) Find the tension forces in each cable: TAQand TBQ(kN}. Neglect the mass of the cables, but include the mass of the boom in addition to load P. (b) Find the average stress (s) in each cable.Space Frame ABC is clamped at A, except it is free to rotate at A about the x and y axes. Cables DC and EC support the frame at C. Force Py= - 50 lb is applied at the mid-span of AS, and a concentrated moment Mx= -20 in-lb acts at joint B. (a) Find reactions at support A. (b) Find cable tension Forces.
- A bar ABC revolves in a horizontal plane about a vertical axis at the midpoint C (see figure). The bar, which has a length 2L and crass-sectional area A, revolves at constant angular speed at. Each half of the bar (AC and BC) has a weight W, and supports a weight W2at its end. Derive the following formula for the elongation of one-half of the bar (that is. the elongation of either AC ar BC). =L223gEA(w1+3w2) in which E is t he modulus of elasticity of the material of the bar and g is the acceleration of gravity.Space frame A BCD is clamped at A, except it is Free to translate in the .v direction. There is also a roller support at D, which is normal to line CDE. A triangularly distributed Force with peak intensity q0 = 75 N/m acts along AB in the positive - direction. Forces Px= 60 N and Pz = = 45 N are applied at joint C, and a concentrated moment My = 120 N . m acts at the mid-span of member BC. (a) Find reactions at supports A and I). (b) Find internal stress resultants N. E’I T, and .11 at the mid-height of segment AB.A uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has a stiffness k[= 300 N/m and natural length Lt=250 mm. The corresponding quantities for the spring on the right are k2= 400 N/m and L^ = 200 mm. The distance between the springs is L = 350 mm, and the spring on the right is suspended from a support that is a distance it = SO mm below the point of support for the spring on the left. Neglect the weight of the springs. (a) At what distance x from the left-hand spring (figure part a) should a load P = 18 N be placed in order to bring the bar to a horizontal position? (b) If P is now removed, what new value of k{is required so that the bar (figure part a) will hang in a horizontal position underweight If? (c) If P is removed and kt= 300 N/m. what distance b should spring ktbe moved to the right so that the bar (figure part a) will hang in a horizontal position under weight II"? (d) If the spring on the left is now replaced by two springs in series (kt= 300 N/m, kt) with overall natural length Lt= 250 mm (see figure part b). what value of k; is required so that the bar will hang in a horizontal position under weight IF?