Mechanics of material Tutorial with Solution
Homework 2.1 A plastic wire is pulled by a tensile force of 4 N, and its length increases by 1%. If the plastic has elastic modulus of 4 GPa. Assuming deformation is well within elastic limit, please calculate (a) average normal stress in the wire and (b) the diameter of wire.
Homework 2.2 The 4 mm diameter metal wire EF has modulus E = 200 GPa. If the maximum stress should not be higher than 250 MPa, and the elongation of the wire should NOT be longer than 5 mm. Please calculate the maximum load P can be applied.
Homework 2.3 (1) Members CD and BC have common E = 29 106 psi and cross-section area of 0.75 in2 and 0.6 in2 , respectively. For the forces shown, determine the elongation of (a) CD and (b) BC.
Homework 2.4 A centric load of P=400 kN is applied to the composite block shown through a rigid end plate. The iron plate (EFe=200 GPa) is sandwiched between two Cu plates (ECu=80 GPa). Center iron plate is 40 mm thick while the outer Cu plates are 20 mm thick. All plates are 500 mm long and 100 mm wide, Calculate the normal stress in the center Fe core and the outer Cu plates.
Homework 2.5 A rigid bar EH is supported by two steel wire of 1/16 in diameter (E=29 106 psi) and a pin and bracket at H. Knowing that the wires were initially tight. Determine (a) the additional tension in each wire when a 200-lb load P is applied at E. (b) The corresponding deflection (downward displacement) of point E.
Homework 2.6 (1) A tensile force of 2 kN is applied to a test steel (E = 200GPa, ν = 0.30) bar with rectangular cross-section with initial thickness of 2 mm, initial width of 10 mm, and initial length of 100 mm. Please calculate the absolute change in (a) sample length, (b) sample thickness, (c) sample width, and (d) sample cross-section area.
Homework 2.7 Two blocks of rubber with shear modulus G=10 MPa are bonded to rigid supports and a plate AB as illustrated. c = 100 mm and P = 50 kN. Calculate the minimum value for dimension a and b for the rubber blocks if the shearing stress should not exceed 1 MPa and the deflection of the plate is at least 4 mm.