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- 5. A car is driving down the road and goes over a speed bump. The car has a solid circular drive shaft that is subjected to a tensile axial force of F = 400 kN, a bending moment of M = 10.0 kN·m, and a torque of T = 18.0 kN·m as a result of the bump. The shaft has a diameter d = 10.0 cm and mechanical properties of E = 200 GPa, v = 0.35 and σ = 200 MPa. a. What and where is the maximum stress? Hint: use the principle of superposition. b. What are the principal stresses and their directions? c. If it is a ductile steel, will the shaft yield? d. If it is a brittle steel, will the shaft fail? F M T Marrow_forwardAluminum L= 3 m A = 500 mm² E = 70 GPa A 3.5 m P B Steel L = 4 m A = 300 mm² E = 200 GPa 2.5 m с # 3A. The rigid bar AB, attached to two vertical rods as shown, is horizontal before the load P is applied. Determine the vertical movement of P if its magnitude is 50 kN. #3B. A steel rod is stretched between two rigid walls and carries a tensile load of 5000 N at 20°C. If the allowable stress is not to exceed 130 MPa at -20°C, what is the minimum diameter of the rod? Assume a=11.7μm/(m-°C) and E=200 GPa.arrow_forwardA vibration isolation unit consists of two blocks ofhard rubber bonded to a plate AB as shown. A force ofmagnitude P = 24 kN causes a deflection δ = 1.5 mmof the plate AB.(a) Determine the modulus of rigidity (G)of the rubber used.(b) If a rubber having G = 19 MPa is usedand denoting P the magnitude of the forceapplied to AB and by δ the correspondingdeflection, determine the equivalent springconstant k = P/δ of the system.arrow_forward
- Determine the horizontal displacement of joint C. The length, L, of trusses AC, BC is 1,300 mm. The applied force at joint C, is 5.0 kN. The cross-sectional area of both trusses, A, is 360 mm2. The elastic modulus of truss AC, E1, is 135 GPa. The elastic modulus of truss BC, E2, is 150 GPa.arrow_forwardMechanical Vibration Problem.arrow_forwardA circular rod and a 0.1-in.-thick rectangular bar are both made of a plastic material that has an elastic modulus of E = 2.3 GPa and a Poisson’s ratio of ν = 0.33. The rod and the bar are initially the same length L. After a particular load is applied, the 3.6-in.-wide rectangular bar is elongated by some amount ΔL and its width is reduced by 0.096 in. If the 1.3-in. diameter rod is stretched by the same amount ΔL, determine its change in diameter. Expansion is positive, while contraction is negative.arrow_forward
- Problem (2) A vibration isolation unit consists of two blocks of hard rubber bonded to a plate AB as shown. A force of magnitude P = 24 kN causes a deflection ô = 1.5 mm of the plate AB. (a) 150 mm J00 mm Determine the modulus of rigidity (G) of the rubber used. If a rubber having G= 19 MPa is used (b) and denoting P the magnitude of the force applied to AB and by ô the corresponding deflection, determine the equivalent spring constant k = P/d of the system. 30 mm 30 mmarrow_forwardIn mechanical resistancearrow_forwardThe rigid bar AC is supported by two axial bars (1) and (2). Both axial bars are made of bronze [E = 100 GPa; a = 18 × 10-6 mm/mm/ °C). The cross-sectional area of bar (1) is A1 = 184 mm2 and the cross-sectional area of bar (2) is A2 = 380 mm2. After load P has been applied and the temperature of the entire assembly has increased by 38°C, the total strain in bar (2) is measured as 1240 µɛ (elongation). Assume L1 = 1290 mm, a = 590 mm, b = 820 mm, and L2 = 2000 mm. Determine: (a) the magnitude of load P. (b) the vertical displacement of pin A. L2 (1) L1 B a P Answers: (a) The magnitude of P = i kN. (b) The vertical displacement of pin A = i mm (down).arrow_forward
- In the following structure, determine x, such that the deformation in cable CD is two times that of deformation in cable AB. Assume, both cables are made of the same material (similar E) and have the same cross-sectional area (A).arrow_forwardA car has broken down in the middle of a road. Eva wants to help tow thecar to a mechanic with her 4WD. To avoid the car from slamming into Eva’s 4WD, they attach the front of the car to the back of Eva’s 4WD by a stiff spring.The broken car weighs 2000kg. The spring has a natural unstretched length of 2m and a spring constant of k = 80000N/mFor this particular gravel road, the magnitude of the drag force is proportional to the weight of the car and the speed of the car. The direction of the drag force is always opposite tothe direction of movement. This can be written asD = −cM v For this particular road we can take c = 4. Let x(t) be the position of the front of the broken car and let y(t) be the position of the back of Eva’s 4WD. We will assume that the position of Eva’s car is a known function of time.(1) By considering Newton’s law applied to the broken car, write down an ordinary differential equation for the motion of the broken car They are planning to travel at a constant…arrow_forwardhi please solve this question. (Mechanical )arrow_forward
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