Uniform 40kg bar AB is subjected to force P, smooth guides at B, at A, u,-0.3, (a) If P-200N, find friction force at A. (b) find P required to cause slippage at A. B 112 /2 60A
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- -11 A rubber cube R of a side L = 3 in. and cross- sectional area A = 9 in2 is compressed inside a steel cube S by a force F = 5 lb that applies uniformly distributed pressure to the rubber. Assume E 0.3ksi and,, = 0.45. (a) Calculate the lateral pressure between the rubber and steel (disregard friction between the rubber and the steel, and assume that the steel block is rigid when compared to the rubber). (b) Calculate the change in volume of the rubber.Solve the preceding problem for a W 250 × 44.8 wide-flange shape with L = 3.5 m. q = 45 kN/m, h = 267 mm, b = 148 mm, rt = 13 mm, = 7.62 mm, d = 0.5 m, and a = 50 mm.Problem :Pressure vessel made of alloy steel with Yield Strength of 250 MPa, Pressure acting on Pressure Vessel = 10 Atmosphere. Longitudinal Stress (σL) = 200 MPa. Hoop Stress (σθ) = 150 MPa. Radial Stress (σR) = -50. Question :a) How thick is the pressure vessel if the Inner Diameter is D = 2 Meters? b) Check whether the pressure vessel is safe or not? c) Calculate the maximum shear stress with Mohr's circle? d) Check whether the pressure vessel is safe or not with Tresca yield criterion and compare it with von Mises yield criterion?
- P1 is the critical point. If the maximum permissible tensile stress is 150 MPa and themaximum permissible in-plane shear stress is 55 MPa, what is the largest load, P, that can beapplied by the rider? Where shaft OD = 32mm and thickness = 3.25mmA drill drills a hole in a leg of a furniture. Uses a hand-operated drill with a bit of diameter equal to 5.79mm. If the resisting torque supplied by the table is equal to 0.36 N.m, what is the maximum shear stress of the drill bit? If the allowable shear stress in the drill bit is 44.215MPa, what is the maximum resisting toque before the drill binds up?The axle of a heavy-duty tractor transmits 120 kW at 600 rpm. It acts as a cantilever supporting a load of 280 N located 60 cm from the fixed end. The allowable normal stress is 137 MPa and the allowable shear stress is 62 MPa. If the axial load is negligible, find the axle diameter.
- In the figure, torsional moments act on a bar system of abruptly changing cross-section made of the same material. Accordingly, calculate the value of the factor α so that the support responses are of the same magnitude in absolute value. What must the torsional moment=Mb be for the D-end to be zero? Note: The shear modulus of the material is G = 80 GPa Mo= 10 kNm.A closely coiled helical spring is made of 6 mm diameter steel wire, the mean diameter of the coil is 60 mm and there are 8 coils. Taking the modulus of rigidity as 100 kN/mm2, find the stress, in kPa, in the wire when carrying an axial load of 529N.Imagine that a long steel wire hangs vertically from a high-altitude balloon.(a) What is the greatest length (feet) it can have without yielding if the steel yields at 44) ksi?(b) If the in wire hangs from a ship at sea, what is the greatest length? (Obtain the weight densities of steel and seawater from Table I-I. Appendix I.)
- (Q1) A uniform beam, of mass 31 kg/m run, is simply supported on a span of3.6 m. Taking EI for the beam as 7 MN.m2, calculate the frequency oftransverse vibrations.This frequency is to be reduced by 40% by fixing three equal masses tothe beam, at the mid-point and the quarter points. Calculate how muchthese masses should be. (Q2) A beam 6 m long, simply supported at each end, carries a load of 6 t/mrun, extending from a point 1.2 m from one support to another point 4.2m from the same support. EI for the beam is 110 MN.m2. The mass of thebeam itself may be neglected.Determine the frequency of transverse vibrations of the beam in avertical plane:a) very roughly, assuming the whole load to be concentrated at itscentre of gravity.b) more accurately, by treating the load as three equal concentratedloads applied at suitable points. (Dunkerley's method issuggested.)A rotary blade rotates at 3500 rev/min. The steel blade has a uniform cross section 3 mm thickness by 30 mm in wide, and has a 12 mm-diameter hole in the center as shown in the figure. Estimate the maximum tensile stress at the central section due to rotation. Use steel density as 7800 kg/mA rubber cylinder Rof length L and cross-sectional area A iscompressed inside a steel cylinder S by a force Fthat applies a uniformlydistributed pressure to the rubber (see figure).(a) Derive a formula for the lateral pressure p between the rubber andthe steel. (Disregard friction between the rubber and the steel, andassume that the steel cylinder is rigid when compare d to the rubber.)(b) Derive a formula for the shortening 6 of the rubber cylinder.