ΠΗ 6.14 Determine the nodal displacements and the element stresses, including prin- cipal stresses, due to the loads shown for the thin plates in Figure P6-14. Use E = 105 GPa, v = 0.30, and t = 5 mm. Assume plane stress conditions apply. The recommended discretized plates are shown in the figures. Use a computer program to solve these. 5 500 mm (a) 3 2 20 kN 3 250 mm 5 100 mm 30° 40 kN 100 mm (b) 2 20 kN

-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.

Acting on the sides of a stress element cut from a bar in uniaxial stress are tensile stresses of 10,000 psi and 5000 psi, as shown in the figure. (a) Determine the angle 0 and the shear stress T and show all stresses on a sketch of the element. (b) Determine the maximum normal stress amaxand the maximum shear stress Tmax in the material.

The stresses acting on a stress element on the arm of a power excavator (see figure) are ax= 52 MPa and txy= 33 MPa (sec figure). What is the allowable range of values for the stress if the maximum shear stress is limited to = 37 MPa?

The normal and shear stresses acting on element A are 6500 psi, 17,300 psi, and 2900 psi (see the figure b for Problem 7.2-5). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element.

A punch for making a slotted hole in ID cards is shown in the figure part a. Assume that the hole produced by the punch can be described as a rectangle (12 mm X 3 mm) with two half circles (r = 1.5 mm) on the left and the right sides. If P = 10 N and the thickness of the ID card is 1 mm, what is the average shear stress in the card?

A circle of a diameter d = 200 mm is etched on a brass plate (see figure). The plate has dimensions of 400 x 400 x 20 mm. Forces are applied to the plate, producing uniformly distributed normal stressescr^ =59 MPaander^ = —17 MPa. Calculate the following quantities: (a) the change in length Aac of diameter at: (b) the change in length Abd of diameter bd; (c) the change At in the thickness of the plate; (d) the change AV in the volume of the plate; (e) the strain energy U stored in the plate; (f) the maximum permissible thickness of the plate when strain energy £/must be at least 784 J; and (g) the maximum permissible value of normal stress axwhen the change in volume of the plate cannot exceed 0.015% of the original volume. (Assume E = 100 GPa and v = 0.34

Solve the preceding problem for the following data: diameter LO m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa. and Poisson's ratio 0.29

An element in plane stress from the fuselage of an airplane is subjected to compressive stresses of magnitude 35 MPa in the horizontal direction and tensile stresses of magnitude 6.5 MPa in the vertical direct ion. Also, shear stresses of magnitude 12.5 MPa act in the directions shown (see the figure for Problem 7.2-8). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element.

An element in plane stress is subjected to stresses sx= -5500 psi, sy= -2000 psi, and Tx. = 1900 psi (see the figure for Problem 7.3-1). Determine the principal stresses and show them on a sketch of a properly oriented element.