A frame structure is shown in the following Figure. Members ABC and BD are pin jointed to supports at A and D, respectively. An external load 4kN is applied vertically at point C. Find the magnitude of the force member BD? (Note, the member BD is a two-force body) O O O O O 4 kN Don't Know 24 kN 16 KN 8 kN 30% 4m B 4m 4kN C
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- 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).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..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 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.A soccer goal is subjected to gravity loads (in the - z direction, w = 73 N/m for DG, BG, and BC; w = 29 N/m for all other members; see figure) and a force F = 200 N applied eccentrically at the mid-height of member DG. Find reactions at sup ports C, D, and H.A space truss is restrained at joints O, A. B. and C, as shown in the figure. Load P is applied at joint A and load IP acts downward at joint C. (a) Find reaction force components Ax, By, and B. in terms of load variable P. (b) Find the axial force in truss member AB in terms of load variable P.
- A plane frame with a pin support at A and roller supports at C and £ has a cable attached at E. which runs over Frictionless pulleys al D and B (see figure). The cable force is known to be 400 N. There is a pin connection just Lo the left of joint C. (a) Find reactions at supports^, C, and E. (b) Find internal stress, resultants N, V, and M just to the right of joint C. (c) Find resultant force in the pin near C.A long re Lai nine: wall is braced by wood shores set at an angle of 30° and supported by concrete thrust blocks, as shown in the first part of the figure. The shores are evenly spaced at 3 m apart. For analysis purposes, the wall and shores are idealized as shown in the second part of the figure. Note that the base of the wall and both ends of the shores are assumed to be pinned. The pressure of the soil against the wall is assumed to be triangularly distributed, and the resultant force acting on a 3-meter length of the walls is F = 190 kN. If each shore has a 150 mm X 150 mm square cross section, what is the compressive stressA plane frame is restrained al joints A and C, as shown in the figure. Members AB and BC are pin connected at B. A triangularly distributed lateral load with a peak intensity or 90 lb/ft acts on AB. A concentrated moment is applied at joint C. (a) Find reactions at supports A and C. (b) Find internal stress resultants A', V, and \f at x = 3 ft on column AB.
- 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 rigid bar of weight W = SOO N hangs from three equally spaced vertical wines( length L = 150 mm, spacing a = 50 mm J: two of steel and one of aluminum. The wires also support a load P acting on the bar. The diameter of the steel wires is ds= 2 mm, and the diameter of the aluminum wire is d = A mm. a Assume £,=210 GPa and EB« 70 GPa. What load Pallowcan be supported at the mitl-point of the bar (x = a) if the allowable stress in the steel wires is 220 MPa and in the aluminum wire is 80 MPa? (See figure part (b) What is /*,Ikw» if the load is positioned at .v = all1? (See figure part a.) (c) Repeat part (b) if the second and third wires are switched as shown in the figure part b.A steel cable with a nominal diameter of 25 mm (see Table 2-1) is used in a construction yard to lift a bridge section weighing 38 kN. as shown in the figure. The cable has an effective modulus of elasticity E = 140 GPa. (a) If the cable is 14 m long, how much will it stretch when the load is picked up? (b) If the cable is rated for a maximum load of 70 kN, that is the factor of safety with respect to failure of the cable?