The principal stresses at a point a stressed material are 2 01= 200 N/mm², 02= 150 N/mm2, and 02= 200 N/mm². E = 210 kN/mm² and m = 0.3 The volumetric strain will be
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Q: 200 500 B 1100 T(N-m) 900
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Principal stress, solid mech.
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- A flat bar with a cross section of 8 mm by 50 mm elongates 2.1 mm in a length of 1.5 m as a result of an axial load of 50 kN. The proportional limit of the material is 240000 KN/sq m. Determine the axial stress in the bar and the modulus of elasticityThe wooden section of the beam is reinforced with two steel plates as shown. If the beam is subjected to a moment of M = 5.0 kN. m, determine the maximum bending stresses in the steel and wood. Sketch the stress distribution over the cross section. Take Ew = 11 GPa and Est = 200 GPaThe rigid, horizontal slab is attached to two identical copper rods. There is a gap ∆ = 0.18 mm between the middle bar, which is made of aluminum, and the slab. Neglecting the mass of the slab, calculate the stress in each rod when the temperature in the assembly is increased by 60 oC. Use the following data:
- The rigid horizontal slab is attached to two identical copper rods. There is a gap Δ = 6.18 mm between themiddle bar, which is made of aluminum, and the slab. Neglecting the mass of the slab, calculate the stress in each rod when the temperature in the assembly is increased by 81°C. Use the following data:The concrete tower of a water tank with a cross section in the form of a circular ring carries the weight of the full tank as load F shown in the figure. a) If the allowable compressive stress for the concrete is 8 MPa, determine the maximum capacity of the water tank as cubic meter. b) Considering the weight of the water tank and the weight of the tower itself, determine the shortening Dl of the tower. c) Determine the compressive stress distribution along the tower. (Mass density and the elastic modulus of the concrete are pc=2400 kg/m3 and Ec=12 GPa respectively)The stresses shown act at a point on the free surface of a machine component. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 22 ksi, Sy = 1.5 ksi, and Sxy = 5.2 ksi. Assume β=21∘. Determine the normal stresses σx and σy and the shear stress τxy at the point.
- A steel pipe of length L = 4.0 ft, outside diameter = 6.0 in., and inside diameter = 4.5 in. is compressed by an axial force P kips. The material has modulus of elasticity E = 30,000 ksi and Poisson’s ratio υ = 0.30. Determine the following quantities for the pipe: (a) the shortening, (b) the lateral strain (c) the increase in the outer diameter and the increase in the inner diameter, and (d) the increase in the wall thickness. (Where P=55)The stresses shown act at a point on the free surface of a machine component. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 12.4 ksi, Sy = 3.5 ksi, and Sxy = 3.6 ksi. Assume B = 29°. Determine the normal stresses ox, and oy, and the shear stress rxy, at the point.An 18-m-long steel wire of 10-mm diameter is to be used in the manufacture of a prestressed concretebeam. It is observed that the wire stretches 55 mm when a tensile force P is applied. Knowing that E=250GPa, determine (a) the magnitude of the force P, (b) the corresponding normal stress in the wire
- At a point in a machine component that is subjected to plane stress, the normal and shear stresses are σx= 100 MPa, σy= 65 MPa, and τxy= 70 MPa, acting in the directions shown in the figure. At this point, determine the strain components εx, εy, εz, and γxy. Assume that E = 71 GPa and v = 0.28 for the machine component.At a point in a machine component that is subjected to plane stress, the normal and shear stresses are σx=σx= 200 MPa, σy=σy= 80 MPa, and τxy=τxy= 28 MPa, acting in the directions shown in the figure. At this point, determine the strain components εx, εy, εz, and γxy. Assume that E = 69 GPa and v = 0.31 for the machine component.The principal stresses in the wall of a container are 40 MN/mm² and 80 MN/mm². The normal makes an angle of 30° with a direction of maximum principal stress. The resultant stresses in the plane will be ?