al Ignoring the self-weight of the members, determine the support reactions.
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- .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).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.
- The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress ?? =6.5×10-6 /? is produced in the rails when they are heated by the sun to 120"F if the coefficient of thermal expansion a = the modulus of elasticity E = 30 × 106 psi?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 stressThe truss ABC shown in the figure supports a vertical load W at joint B. Each member is a slender circular steel pipe (E = 30,000 ksi) with an outside diameter of 4 in. and wall thickness 0.25 in. The distance between supports is 23 ft. Joint B is restrained against displacement perpendicular to the plane of the truss. Determine the critical value Wcr of the load.
- An aluminum [E = 10,000 ksi] control rod with a circular cross section must not stretch more than 0.22 in. when the tension in the rod is 2100 lb. If the diameter of the rod is 0.372 in., determine the maximum length of the rod.A 5.0m long steel wire has a cross-sectional area of 0.55cm^2. Its proportional limit has a value of 0.0018 times its Young's modulus. Its breaking stress has a value of 0.0065 times its Young's modulus. The wire is fastened at its upper end and hangs vertically. a. How great a weight can be hung from the wire without exceeding the proportional limit? b. How much will the wire stretch under this load? c. What is the maximum weight that the wire can support?L₁ B 7 B D -‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒ T Figure 1. Boom of a crane supporting load T. The boom of the crane ABC shown in Figure 1 is pin supported at A. The hydraulic support BD can be assumed as a two-force member. It carries load only along its axis. Calculate the reaction forces at the pin support and the reaction force exerted by BD on the boom. The data required to solve the problem are: L₁ 4.5 m, L₂ = 4 m, a = 60°, B = 50° and T = 34 kN. =
- In the figure showing 3 pieces of steel bar (Member AB, CD, EF) receiving rigid steel beam AE (Rigid Beam) with the appearance of a pin connection to bear the weight of the force P at point G by the size of the force P ( unit kN) equal to 90. Given that the cross-sectional area of Member AB and EF = 1000 mm, and the area of CD = 500 mm and the Modulus of Elasticity (E) = 200 GPa, answer the questions and show the calculation as follows: 1.1 Shown The equilibrium equation related to the above problem Determinate or Indeterminate Why? 1.2 Show the Condition of Deformation or Compatibility related to the problem in 1.1 1.3 Show the calculation for the internal force of Member AB, CD, EF and stress or axial force and indicate that the problem is considered to be Maximum statically stressed (Maximum Axial Stress). 1.4 Calculate the maximum vertical displacement of Rigid Beam AE1. A prismatic bar AE of negligible weight is hinged to a vertical wall at A and supported by a strut BD as shown in Fig. 1. Find the reaction induced at A and B through the action of a sphere of weight W tied by a string CF that is parallel to AE. Also, find the tension in the string. The radius of the sphere is such that the points B and C are at the same level. Assume W = 1000 lb.05:54 PMThe load per foot of beam length varies as shown. For x = 18 ft, the unit load is 601 lb/ft. At x = 0, the load is increasing at the rate of 51 lb/ft per foot. Calculate the support reactions at A and B. The reactions are positive if upward, negative if downward. [Answer: RA = 2280 ft, RB = 4080 lb]