When there is a plane stress condition as shown in the figure, display this stress in the form of the maximum in-plane shear stress and the corresponding average vertical stress.

The stresses shown act at a point in a stressed body. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are S, = 20 MPa, S, = 24 MPa, and Sy = 29 MPa. Assume ß = tan = 21.8°, a = 5, and b = 2. Using the equilibrium equation approach, determine the normal and shear stresses o (positive if tensile, negative if compressive) and z (magnitude only) at this point on the inclined plane shown. Answers: i MPa, T = i MPа.

3. An element in plane stress on the fuselage of an airplane (figure part a) is subjected to compressive stresses of magnitude 35 MPa in the horizontal direction and tensile stresses of magnitude 10.5 MPa in the vertical direction (see figure part b). Also, shear stresses of magnitude 12.5 MPa act in the directions shown. Determine the stresses acting on an element oriented at a clockwise angle of 40° from the horizontal. Show these stresses on a sketch of an element oriented at this angle. (a) 10.5 MPa Ţ (b) 35 MPa 12.5 MPa

a. Determine the principal stresses at point A on the cross section of the wrench at section a-a. Also Specify the orientation for this state of stress. b. Determine maximum in-plane shear stress at point A on the cross section of the wrench at section a-a. Also Specify the orientation for this state of stress.

Please show full work than you

2. The figure below shows a shaft with pulley and gear. Find the location along the x axis where the normal and shear stresses are the greatest. Create an element drawing of the stress state at this location. Find the principal stresses. Hints:1. the shaft diameter is not given, but you can find the stresses as a function of diameter. 2. Because the shaft is rotating, the maximum normal stress can be determined by using the resultant moment. 1. 622 YA ΤΑ 6 in. - 4 in. Gear/ 600 lb 2000 lb 79 Fp=? 12 in. 200 lb 1 +3 in.-102 D 8 in. Pulley B X

4- Calculate the principal stresses and the maximum shear stress for an element in plane stress and subjected to the stresses as shown in the below figure. 40 MPa 10 MPa 70 MPa

Calculate non-zero stress components (normal and shear) at points A, B and C. Point C is located at the center of the cross section attached to the wall. Calculate non-zero strain components at point B. Neglect shear stress due to shear force. Given: loading F = 400 N, P-2000 N, and T = 75 N·m, Young's modulus E = 70 GPa, Poisson's ratio v = 0.25 15-mm D. -100 mm

Suppose that σ = 330 psi and Try = 150 psi in (Figure 1). Figure Part D Specify the orientation of the principal stress. Take the positive direction of rotation counterclockwise. Express your answer in degrees to three significant figures. Op₁= Part E OF 0₂ = ΑΣΦΙΚΗ vec Specify the orientation of the maximum in-plane shear stress. Take the positive direction of rotation counterclockwise. Express your answer in degrees to three significant figures. 0/ —| ΑΣΦ 11 | vec ? ? o

Q 1-3 Determine the maximum tensile, compressive, and shear stresses at point A on the bicycle pedal crank shownin the figure. The pedal and crank are in a horizontal plane and point A is located on the top of the crank. The load P = 160 lb acts in the vertical direction and the distances (in the horizontal plane) between the line of action of the load and point A are b, = 5.0 in. and b, = 2.5 in. Assume that the crank has a solid circular cross section with diameter d = 0.6 in. P = 160 lb Crank d = 0.6 in. b = 5.0 in. b2 = 2.5 in.