A member of uniform rectangular cross section is subjected to a bending moment M = 36.8 kN-m. The member is made of an elastoplastic material with a yield strength of 240 MPa and a modulus of elasticity of 200 GPa. Determine (a) the thickness of the elastic core, (b) the radius of curvature of the neutral surface. c = 60 mm c = 60 mm b = 50 mm ↑ YY
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- A beam of the cross section shown is made of a steel that is assumed to be elastoplastic with E=29×106psi and σY= 42 ksi. A bending couple is applied to the beam about the z axis, causing plasticzones 2 in. thick to develop at the top and bottom of the beam. After the couple has been removed, determine (a) the residual stress at y=2 in., (b) the points where the residual stress is zero, (c) the radius of curvature corresponding to the permanent deformation of the beam.The solid circular drill rod AB is made of a steel that is assumed to be elastoplastic with τY = 22 ksi and G = 11.2 × 106 psi. Knowing that a torque T = 72 kip·in. is applied to the rod and then removed, determine the maximum residual shearing stress in the rod. The maximum residual shearing stress in the rod is ksi.E al = 70Gpa E cu = 75 Gpa fınd the max stress in both of tow materials in the picture alümünyum = Al Bakır = cu
- Shown is a composite plate joined together by rivets. The components consist of two tension bar plates that is ¾ X 4 inch and riveted together by two splice plates which is 0.8 X 6 inch. Each rivet has a diameter of 25.4 mm. Considering that the allowable stress for the tension bar plates and splice plates is σ=20.0 ksi, the allowable shear stress for the rivets is σ=25.0 ksi and the allowable bearing stress on the rivets and splice plates is σ=25.0 ksi. What will be the maximum permissible load P such that none of the allowable stresses will be exceeded?The composite beam shown in the figure is simply supported and carries a total uniform load of 90 kN/m on a span length of 4 m. The beam is built of a wood member having cross-sectional dimensions 150 mm x 250 mm and two steel plates of cross-sectional dimensions 50 mm × 150 mm. The moduli of elasticity are Es = 214 GPa and Ew = 11 GPa. (a) Determine the maximum stress in the steel. (Disregard the weight of the beam. Round to one decimal place.) (b) Determine the maximum stress in the wood. (Disregard the weight of the beam. Round to one decimal place.)Axial loads are applied to the compound rod that is composed of an aluminum segment rigidly connected between steel and bronze segments. P = 10 kN a. What is the stress (MPa) in the Bronze material? b. What is the stress in Aluminum in MPa? c. What is the stress in Steel in MPa?
- The composite beam shown in the figure is simply supported and carries a total uniform load of 40 kN/m on a span length of 4.0 m. The beam is built of a southern pine wood member having cross-sectional dimensions 150 mm 250 mm and two brass plates of cross-sectional dimensions 30 mm 150 mm. (a) Determine the maximum stresses B and w in the brass and wood, respectively, if the moduli of elasticity are EB 96 GPa and Ew 14 GPa. (Disregard the weight of the beam.) (b) Find the required thickness of the brass plates so that the plate and wood reach their allowable stress values, saB 70 MPa and saw 8.5 MPa, simultaneously under the maximum moment. What is the maximum moment?A RECTANGULAR ALUMINUM BLOCK IS 40mm LONG IN THE Y DIRECTION,20mm WIDE IN THE Z DIRECTION AND 25mm THICK IN THE XDIRECTION. IT IS SUBJECTED TO A TRIAXIAL LOADING CONSISTING OF AUNIFORMLY DISTRIBUTED FORCE OF Px=3kN (COMPRESSION), Py=4kN(TENSION) AND Pz=7kN (COMPRESSION) IN THE X, Y AND Z DIRECTIONSRESPECTIVELY. IF THE POISSON’S RATIO = 1/4 & E = 70 GPa,DETERMINE THE STRAINS IN THE X, Y AND Z DIRECTIONS. ALSODETRMINE A SINGLE DISTRIBUTED FORCE IN THE Y DIRECTION THEWOULD PRODUCE THE SAME X DEFORMATION AS THE ORIGINAL.A composite beam is made of two brass [E = 96 GPa] plates bonded to an aluminum [E = 62 GPa] bar, as shown. The beam is subjected to a bending moment of 2260 N-m acting about the z axis. Assume b=53 mm, d1=48 mm, d2=14 mm. Determine:(a) the maximum bending stresses σbrσbr, σalσal in the brass plates and the aluminum bar.(b) the stress in the brass σbrjσbrj at the joints where the two materials are bonded together.
- Explain stress-strain relationship for mild steel. Discuss in brief about the elastoplastic behaviour in axial loading.The polymer bar shown in the figure below has a width of b=55b=55 mmmm, a depth of d=104d=104 mmmm, and a height of h=274h=274 mmmm. At a compressive load of P=120P=120 kNkN, the bar height contracts by Δh=−2.60Δh=-2.60 mmmm, and the bar depth elongates by Δd=0.36Δd=0.36 mmmm. At this load, the stress in the polymer bar is less than its proportional limit. Determine: (a) the modulus of elasticity. (b) Poisson’s ratio. (c) the change in the bar width bb.The composite shaft shown in the figure is manufactured by shrink-fitting a steel sleeve over a brass core so that the two parts act as a single solidbar in torsion. The outer diameters of the two parts are d1 = 1.6 in. for the brass core and d2 = 2.0 in. for the steel sleeve. The shear moduli of elasticity are Gb = 5400 ksi for the brass and Gs = 12,000 ksi for the steel.(a) Assuming that the allowable shear stresses in the brass and steel are τb = 4500 psi and τs = 7500 psi, respectively, determine the maximumpermissible torque Tmax that may be applied to the shaft.(b) If the applied torque T =15 kip-in., find the required diameter d2 so that allowable shear stress τs is reached in the steel.