Q.1) For the roller support atA and pin support at B, Compute the reactions at.A and B. B Answer. 40 N 50 N 30 N10 N 6 cm 6 cm 10 cm 8 cm
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- Solve the preceding problem for the following data: b = 6 in., b = 10 in, L = 110 ft, tan a = 1/3, and q = 325 lb/ft.Repeat 1.3-9 but use the method of sections go find member forces in AC and BD.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 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 Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.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.
- 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?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.Frame ABC has a moment release just left of joint B. Find axial force N, shear force V, and moment M at the top of column AB. Write variables N, V, and M in terms of variables P and L.
- Solve the preceding problem for a W 250 × 89 steel column having a length L = 10 m. Let E = 200 GPa.A space truss is restrained at joints A, B. and C, as shown in the figure. Load P acts in the +z direction at joint Band in the -z directions at joint C. Coordinates of all joints are given in terms of dimension variable L (see figure). Let P = 5 kN and L = 2 m. (a) Find the reaction force components Az and Bx. (b) Find the axial force in truss member AB.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.