14. A prismatic bar having cross-sectional area A=1200 mm² is compressed by an axial load P = 90kN (see figure (a)). (1) Determine the stresses acting on an inclined section p-q cut through the bar at an angle = 25°. (2) Determine the complete state of stress for 0=25° and show the stresses on a properly oriented stress element. -x P x1 0=25° P=90 kN x 9 14) FACE ab: 0=25°: σ0=-61.6 MPa, t0=28.7 MPa FACE cd: 0=250+90=205°: σ0=-61.6 MPa, t0=28.7 MPa FACE bc: 0=25°-90°-65°: σ0=-13.4 MPa, t0=-28.7 MPa FACE ad: 0=25°+90° 115°: σ0-13.4 MPa, t0=-28.7 MPa

The flat bars shown in parts a and b of the figure are subjected to tensile forces P = 3.0 kips. Each bar a has thickness t = 0.25 in. (a) For the bar with a circular hole, determine the maximum stresses for hole diameters d = 1 in. and d = 2 in. if the width b = 6.0 in. (b) For the stepped bar with shoulder fillets, determine the maximum stresses for fillet radii R = 0.25 in. and R = 0.5 in. if the bar widths are b = 4.0 in. and c = 2.5 in.

-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.

The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting on an element oriented at an angle 0 = 250. Show these stresses on the rotated element.

At a point on the web of a girder on a gantry crane, the stresses acting on the x face of a stress element are s= 6250 psi and ??xy= 1425 psi (see figure). What is the allowable range of values for the stress ??. if the maximum shear stress is limited to t0 = 2150 psi?

A plastic bar of rectangular cross section (ft = 1.5 in. and h = 3 in.) fits snugly between rigid supporls at room temperature (68oF) but with no initial stress (see Figure). When the temperature of the bar is raised to 160oF, the compressive stress on an inclined plane pq at mid-span becomes 1700 psi. (a) What is the shear stress on plane pq? (Assume a = 60 × 10-6/*t and E = 450 × 103psi.) (b) Draw a stress element oriented to plane pq and show the stresses acting on all laces of this element. (c) If the allowable normal stress is 3400 psi and the allowable shear stress is 1650 psi. what is the maximum load P (in the positive x direction), which can be added at the quarter point (in addition to thermal effects given) without exceeding allowable stress values in the bar?

An aluminum tube is required to transmit an axial tensile force P = 33 k (sec figure part a). The thickness of the wall of the tube is 0.25 in. (a) What is the minimum required outer diameter d minif the allowable tensile stress is 12.000 psi? (b) Repeat part (a) if the tube has a hole of a diameter J/10 at mid-length (see figure parts b and C).

The flat bars shown in parts a and b of the figure are subjected to tensile forces P = 2.5 kN. Each bar has thickness t = 5.0 mm. (a) For the bar with a circular hole, determine the maximum stresses for hole diameters d = 12 mm and d = 20 mm il" the width h = 60 mm. (b) For the stepped bar with shoulder fillets, determine the maximum stresses Tor fillet radii R = 6 mm and R = 10 mm if the bar widths are h = 60 mm and c = 40 mm.

A short column with a wide-flange shape is subjected to a compressive load that produces a resultant force P = 55 kN acting at the midpoint of one flange (see figure). Determine the maximum tensile and compressive stresses asand o^., respectively, in the column, Locate the neutral axis under this loading condition. Recompute maximum tensile and compressive stresses if a 120 mm X 10 mm cover plate is added to one flange as shown.

Two bars AC and BC of the same material support a vertical load P (see figure). The length L of the horizontal bar is fixed, but the angle fl can be varied by moving support A vertically and changing the length of bar AC to correspond with the new position of support A. The allowable stresses in the bars are the same in tension and compression. When the angle ft is reduced, bar AC becomes shorter, but the cross-sectional areas of both bars increase because the axial forces are larger. The opposite effects occur if the angle 0 is increased. Thus, the weight of the structure (which is proportional to the volume) depends upon the angle ft. Determine the angle ft so that the structure has minimum weight without exceeding the allowable stresses in the bars. Note: The weights of the bars are very small compared to the force P and may be disregarded.