A cross section of an engineering structure made of steel is shown in the Figure. For an applied torque of T = 175 N.m, (a) determine how much torque is carried by each of the two cross-sectional components and (b) the angle of twist per unit length. The shear modulus G = 200 GPa. (Neglect the stress concentrations). 45 mm 40 mm 4 mm 60 mm 4 mm 4 mm 120 mm 6 mm

Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 280 psi in size. (a) Determine the stresses Ox, Oy, and the magnitude of Tyand show them on a stress element. (b) Determine the principal stresses and the magnitude of the maximum in-plane shear stress acting at the point and show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16). y Answer: (a) Ox = i ! psi Oy= i ! psi %3D Txy = psi (b) Op1 = i psi Op2 = i psi Tmax in-plane psi

Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 540 psi in size. (a) Determine the stresses Ox, Oy, and the magnitude of Txy and show them on a stress element. (b) Determine the principal stresses and the magnitude of the maximum in-plane shear stress acting at the point and show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16). Answer: (a) ox= i Oy= i Txy = (b) Op1 = Op2 i Tmax in-plane y C psi psi psi X psi psi psi σ

A 52-kip force acts on a machine part at point A as shown below. The diagram shows the internal normal force, shear force and bending moment acting on a particular RECTANGULAR Cross section. -30in N 10in 26in F=52 kip The value of the bending moment M you would use to find the bending stress on a stress element located 2 inches up from the bottom of the rectangular cross section is closest to: 264 kip-in O a. 408 kip-in Ob. 1,464 kip-in O c. 1,608 kip-in

Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 220 psi in size. (a) Determine the stresses Ox, Oy, and the magnitude of Txy and show them on a stress element. (b) Determine the principal stresses and the magnitude of the maximum in-plane shear stress acting at the point and show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16). Answer: (a) ox= i Oy = Txy = i i (b) Op1 = i op2 = i max in-plane y i C psi psi psi X psi psi psi σ

Thin square plate PQRS is symmetrically deformed into the shape shown by the dashed lines in the figure.[a = 200 mm, b = 202.1 mm, c = 198.9 mm] For the deformed plate, determine the normal strain of diagonal PR? In micro £ For the deformed plate, determine the shear strain xy at corner P?in micro rad

A thin rectangular plate ABCD is deformed into a parallelogram as shown in the figure below.  The width of the plate is w = 1300 mm, and the height of the plate is h = 1700 mm.   The shear strain at A is known to be +4172 μrad.  Assume a = 2.9 mm.  Calculate the magnitude of dimension b in the figure.

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The cross-sectional dimensions of a beam are shown in the figure. (a) If the bending stress at point K is 35 MPa (C), determine the internal bending moment Mz acting about the z centroidal axis of the beam. (b) Determine the bending stress at point H. The bending stress is positive if in tension and negative if in compression. 85 mm 4 mm TT K 55 mm H 4 mm 45 mm 4 mm Answers: (a) Mz = UN-m (b) OH = JMPA

The tubular shaft shown in the figure has an external diameter of D = 5.5 in. and an internal diameter of d = 2.75 in. and is subjected to a torque of T= 6825 lb-in. [theta = 31 deg] What is the shear stress at A?in psi What is the shear stress at B?in psi What is the shear stress at C? What is the shear stress at D?in psi What is the shear stress at E?in psi