The space truss above is supported by ball-and-socket joint at points A, B, and E. A single force F = {-200i +300j +50k} N is applied at point D. Take the following: • UDA = {-0.267i -0.802j -0.535k} • UDB = {+0.923i +0.231j -0.308k} • UDc = {-0.371i +0.557j -0.743k} Which of the following is closest to the force in member DB?
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- A space truss is restrained at joints O, A,B, and C as shown in the figure. Load F is applied at joint A and load 2F acts downward at joint C. Each member is a slender, circular pipe (E = 10,600 ksi) with an outside diameter of 3.5 in. and wall thickness of 0.25 in. Length variable L = 11 ft. Determine the critical value of load variable P (kips) at which member OB fails by Euler buckling.The inclined ladder AB supports a house painter (85 kg) at C and the weight iq = 40 K/m} of the ladder itself. Each ladder rail (t5= 4 mm) is supported by a shoe (ts= 5 mm) that is attached to the ladder rail by a bolt of diameter d = 8 mmA sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure. The poles are being designed to resist a wind pressure of 75 lb/ft" against the full area of the sign. The dimensions of the poles and sign are hx= 20 ft, /r =5 ft, and h = 10 ft. To prevent buckling of the walls of the poles, the thickness e is specified as one-tenth the outside diameter d. (a) Determine the minimum required diameter of the poles based upon an allowable bending stress of 7500 psi in the aluminum. (b) Determine the minimum required diameter based upon an allowable shear stress of 300 psi.
- A steel post (E=30×106) having thickness t = 1/8 in. and height L = 72 in. support a stop sign (see figure), where s = 12.5 in. The height of the post L is measured from the base to the centroid of the sign. The stop sign is subjected to wind pressure p = 20 lb/ft2 normal to its surface. Assume that the post is fixed at its base. What is the resultant load on the sign? (Sec Appendix E, Case 25, for properties of an octagon, n =8.) What is the maximum bending stress in the post? Repeat part (b) if the circular cut-outs arc eliminated over the height of the post.The hoisting arrangement for lifting a large pipe is shown in the figure. The spreader is a steel tubular section with outer diameter 70 mm and inner diameter 57 mm. Its length is 2.6 m, and its modulus of elasticity is 200 GPa. Based upon a factor of safety of 2.25 with respect to Euler buckling of the spreader, what is the maximum weight of pipe that can be lifted? (Assume pinned conditions at the ends of the spreader.)The roof over a concourse at an airport is supported by the use of pretensioned cables. At a typical joint in the roof structure, a strut AB is compressed by the action of tensile forces Fin a cable that makes an angle = 75° with the strut (see figure and photo). The strut is a circular tube of steel (E = 30,000 ksi) with outer diameter d2= 2.5 in. and inner diameter d1= 2.0 in. The strut is 5.75 ft long and is assumed to be pin-connected at both ends. Using a factor of safety n = 2.5 with respect to the critical load, determine the allowable force F in the cable.
- An idealized column is composed of rigid bars ABC and CD joined by an elastic connection with rotational stiffness ßRIat C. There is a roller support at B and an elastic support at D with translationa1 spring stiffness ß and rotational stiffness ßR2. Find the critical buckling loads for each of the two buckling modes of the column. Assume that L = 3 m, ß = 9 kN/m, and ßR]= ßR1= ßL2. Sketch the buckled mode shapes.The plane truss shown in the figure supports vertical loads F at joint D, 2F at joint C, and 3F at joint B. Each member is a slender circular pipe (E = 70 GPa) with an outside diameter of 60 mm and wall thickness of 5 mm. Joint B is restrained against displacement perpendicular to the plane of the truss. Determine the critical value of load variable F(kN) at which member BF fails by Eu1er buckling.A vertical pole of aluminum is fixed at the base and pulled at the top by a cable having a tensile force T(see figure). The cable is attached at the outer edge of a stiffened cover plate on top of the pole and makes an angle a = 20° at the point of attachment. The pole has length a = 2.5 m and a hollow circular cross section with an outer diameter d2= 280 mm and inner diameter d1= 220 mm. The circular cover plate has diameter 1.5d2 Determine the allowable tensile force Tallow in the cable if the allowable compressive stress in the aluminum pole is 90 MPa.
- Continuous cable A DB runs over a small friction less pulley al D to support beam OABC, which is part of an entrance canopy for a building (see figure}. The canopy segment has a weight W = 1700 lb that acts as a concentrated load in the middle of segment AB. (a) What is the maximum permissible value of load P at C if the allowable force in the cable is 4200 lb? (b) If P = 2300 lb, what is the required diameter of pins A, B, and D? Assume that the pins are in double shear and the allowable shear stress in the pins is 10 ksi.A pinned-end strut of aluminum (E = 10,400 ksi) with a length L = 6 ft is constructed of circular tubing with an outside diameter d = 1 in. (sec figure). The strut must resist an axial load F = 4 kips with a factor of safety n = 2.0 with respect to the critical load. Determine the required thickness t of the tube.The 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.