1Fry o, = 105 MPa PROBLEM 7.2-24 unnmeiaunue hennnen

A plastic bar of diameter d = 32 mm is compressedin a testing device by a force P = 190 N thatis applied as shown in the figure.(a) Determine the normal and shear stresses actingon all faces of stress elements oriented at (1) anangle θ = 0°, (2) an angle θ = 22.5°, and (3) anangle θ = 45°. In each case, show the stresses ona sketch of a properly oriented element. Whatare σmax and τmax? (b) Find σmax and τmax in the plastic bar if a recenteringspring of stiffness k is inserted intothe testing device, as shown in the figure. Thespring stiffness is 1/6 of the axial stiffness of theplastic bar.

An element in plane stress is subjectedto stresses σx = -8400 psi, σy =1100 psi , andτxy =-1700 psi (see figure). The material is aluminumwith modulus of elasticity E =10,000 ksi andPoisson’s ratio n = 0.33.Determine the following quantities: (a) the strainsfor an element oriented at an angle θ = 30°, (b) theprincipal strains, and (c) the maximum shear strains.Show the results on sketches of properly orientedelements.

principal stress is 10 kPa, then the normal stress stress, is shown in the figure below. If the minimum The state of stress at a point, for a body in place o (in kPa) is = 50 kPa 0,= 100 kPa %3D X,

QUESTION 3 Two vertical forces are applied to a beam as in Figure Q3(a) with the cross section shown in Figure Q3(b). Determine the maximum tensile and compressive stresses in portion BC of the beam. 15 N 3 mm 3 mm 3 mm В 15 N 6 mm 40 mm 60 mm 2 mm A-B 40 mm 40 mm B-C 60 mm C-D 40 mm (b) (a) Figure Q3

The figure above are two rods attached to a rigid bar AB with negligible mass . A MN kN load was applied at the end of this bar. The computed stresses for steel and bronze are Blank 1 mPa and Blank 2 mPa respectively. MN = 48

Vertical load is applied to point B of a 10 mm radius cylindrical bar as shown in the figure. Calculate the normal stress at point A.

4- The cross-section of the ABCD element in the figure is a circle with a diameter of 6 cm. The force of P-500 N is in the x-z plane. The CD segment is parallel to the y-axis. In line with the information given, a- Find the most critical points in section A. b- Calculate the normal and shear stresses at the most critical points in section A. c- Calculate the principal stresses at the specified points. d- Check the section with the Tresca Hypothesis. em = 95 MPa 75 cm B A N 50 cm 10 40 cm P

The cantilever beam with a rectangular cross-section is under the loading P as shown in the figure. P Part A At an arbitrary cross-section, a - a the state of stress is obtained at various points (point 1 - 5, where point 3 is the midpoint). Select all that describe the stress at the cross-section a - a correctly. O The cross-section a-a has three internal loadings, i.e., shear force, normal force, and bending moment. O The normal stress by bending moment at point 5 is zero. O The maximum shear stress by shear force occurs at the same point as the maximum normal stress by bending moment. O The maximum shear stress by shear force occurs at point 3. O Point 1 develops compressive normal stress by bending moment. O The shear stress by shear force at point 1 is zero. Submit Request Answer

A rectangular bar having width w = 6.50 in. and thickness t = 1.25 in. is subjected to a tension load P, as shown in the figure. The %3D magnitudes of the normal and shear stresses on plane AB must not exceed 16 ksi and 7 ksi, respectively. Determine the maximum load P that can be applied without exceeding either stress limit. Assume a = 3 and b = 4. A P a b B Answer: P = i kips %3D