A frame consists of four L-shaped members connected by four torsional springs, each of constant K. Knowing that equal loads P are applied at points A and D as shown, determine the critical value Pcr of the loads applied to the frame. Hint: What is the FBD of a segment of the frame say EAH in the deflected position? What is the moment equation about say E? EK B H K K
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- The rigid arm AB is attached to the end of the solid circular steel rod BC. The rod is supported by bearings at B and a fixed support at C. The bearings at B prevent rod BC from translating up, down, left, or right, but the bearings do allow rod BC to rotate freely about the x axis at B. It is required that the vertical deflection of point A not exceed 0.25 in. when a load of P = 700 lb is applied at A. Determine the minimum diameter needed for rod BC. Use a = 18 in. and b = 45 in. The modulus of rigidity of the rod is G = 11×106 psi. A P Answer: dmin = i a B b in. CTwo solid cylindrical rods support a load of P = 17 kN as shown. Determine the axial load in rod (1).A safety valve spring having 9 and 2 coils has the ends squared and ground. The outside diameter of the coil is 115 mm and the wire is 13 mm. It has a free length of 203 mm. The length of which this spring must be initially compressed to hold a boiler pressure of 1.38 MPa on the seat of 32 mm diameter. Modulus of rigidity is taken as G=80GN/m?. a. Find the force acting on the valve set. b. Determine the mean diameter c. Determine the spring index d. Find the spring deflection e. Find the operating length f. Calculate the solid length g. Calculate the deflection of solid length h. Compute the solid force i. Compute the Wahl factor
- Two solid cylindrical rods support a load of P = 25 kN as shown. Determine the axial load in rod (1). 3.8 m 4.6 m (1) 5.6 m (2) 3.3 m 28.01 kN 19.30 KN 26.06 kN 16.60 kN O 20.32 kN B P2..Assume that the cable GBH is replaced by a cable GB only (TBH-0). So the frame ACD is supported by ball-and-socket joints at A and D and by the cable GB. You know that the frame supports at C a load of magnitude of 268 N. Find the tension in the cable GB. CopMan se reared for praticion or decay 0.925 m 0.35 m 0.5 m 0.5 m 0.875 m H 0.75 m 0.75 mThe rigid bar of negligible mass, pinned at one end, is supported by a steel rod and aluminum rod asshown. What maximum load P can be applied without exceeding stress in the steel of 130MN/m2or in the aluminum of 90MN/m2
- Determine magnitue, angle of the resultant force and location of it from E, considering the structural element having a seif weight of W KN/m (Where, W=1+3). Also calculate support reactions at A and E by using equilibrium equations. 40 kN 80 kN 50 LN te to E 3m 3m 5m 5m Fig-03 Hints: Self weight acts as uniformly distributed load throughout the length. While calculating moments, the action of total self-weight will be considered to be working right at the mid point of the beam.Two steel shafts (G = 77.2 GPa) are connected to a coupling disk B and to fixed supports at A and C. Shaft BC is solid, while shaft AB is hollow with an inner diameter of 25 mm. Take T = 1.1 kN·m. Calculate the reaction at support A and CFor the load diagram shown, determine the Reaction at B, Rg P = 10 kN X1=1.8 m X2=1.05 m For the load diagram shown, determine the Reaction at A, RA P 10 kN X1=1.8 m X2=1.05 m X2
- The truss shown below is composed entirely of steel tubes (Gystens = Gy,scomp = 200 MPa) having a circular cross section, with an outer diameter of 40 mm and an inner diameter of 30 mm. The truss is supported by a pin at A and a roller at 8 kN 10 kN E. Loads are applied at joints B, C, and D as 4 kN shown. BY 3 kN- The support reactions are (axes shown): Ax = -3 kN; Ay = 8.87 kN; E, = 13.13 kN 1.5 m (a) Determine the axial load in each member of the truss. State if the member is in A 299 SE tension or compression. F 2 m 2 m (b) Solve for the overall safety factor with respect to yielding of the truss.Consider the following showing the three-bar assembly. Nodes 1 and 4 are fixed. At node 2, a horizontal force of 50 kN is exerted. The modulus of elasticity of elements 1 and 2 is 200 GPa and that of element 3 is 110 GPa. Similarly, the area of cross section of elements 1 and 2 is 0.001 m? and that of element 3 is 0.002 m². Determine the reactions at nodes 1 and 4. 50 kN 12 2. 3 14 1 m 1 m 1 m Reaction at node 1 = 30 kN. Rection at node 4 = 20 kN а) b) c) d) II Reaction at node 1 = 25 kN. Rection at node 4 = 25 kN Reaction at node 1 = 42.5 kN. Rection at node 4 = 7.5 kN Reaction at node 1 = 32.81 kN. Rection at node 4 = 17.19 kNQ2. The pin-connected frame is subjected to the force Fas shown. The dimensions are 4-4.0 ft, - 2.6 ft. and -3.9 ft. Member BC is made of steel (E- 29000 ksi), and has rectangular cross-section, with b- 13 in. and h=4.1 in. The supports at B and Cact as pins for x-x axis buckling and as fixed supports for y yaxis buckling. Determine the greatest load F(in the unit of kip) the beam will support without causing member BC to buckle. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Your Answer: