Determine the resulting stress equations for o, Oy, and Try given the Airy stress function Ф = a1x* + a2x°y + a 3x²y² + a4xy³ + a5yª

igure 200 mm 400 mm 20 mm A Section a-a < F₁ 1 of 1 F₂ Determine the state of stress at point A on the cross section of the pipe assembly at section a -a. Take F₁ = 1540 N, F₂ = 1030 N (Figure 1) Express your answer to three significant figures and include the appropriate units. Enter negative value in the case of compression and positive in the case of tension. 4 σA= Part B μA Value Submit Request Answer (Tay) A = Find (Tzy) A- Express your answer to three significant figures and include the appropriate units. μA Units Value Units ? H ?

The stresses shown on the right below act at a point on the surface of a cantilever beam, as shown on the left. Determine the normal and shear stresses at this point on the inclined plane A-B, by drawing a suitable free-body diagram and applying the equations of force equilibrium. A √70° B 5 ksi -20 ksi

The 1900-NN load is applied along the centroidal axis of the member. (Figure 1)   Determine the magnitude of the resultant internal normal force in the member section a-a. Express your answer to three significant figures and include the appropriate units.   2) Determine the magnitude of the resultant internal shear force in the member section a-a.   Express your answer to three significant figures and include the appropriate units.

A stress element in a rock mass making up a slope experiences a 2D stress as follows: σx = 8 MPa, σy = 4 MPa , tauxy = 3 MPa a. Draw the Mohr circle. On Mohr's circle, mark the location of the x and y planes, mark the angle of rotation θ from the x plane to the σ₁,σ3,and taumax plane. Prove that the angle of rotation of the Mohr circle is 2 times the angle of rotation of the element. b. Write down the coordinates of the center of Mohr's circle and calculate its radius.

A 60 ̊ strain rosette measures the following strain at a point on the aluminum skin of an airplane. ε0 = 160 ×10-6 m/m, ε60 = -220 ×10-6 m/m and ε120 = 360 ×10-6 m/m. Using E= 10 ×106 psi and v = 0.3, Determine the principle stresses and the maximum in-plane shear stress.

The drill shown is jammed in the wall and is subjected to the torque and force shown in the diagram. Determine the normal stress (in MPa) at point A on the cross section of the drill bit at section a−a.

The bent shaft is fixed in the wall at A. If a force F is applied at B (the force is acting on the plane parallel to the x-o-y plane). Take F = 54 N and 0 = 45°. 1. Determine the internal forces acting on the section containing points D and E 2. Determine the normal stress component acting at point E 3. Determine the shear stress component developed at point E 4. Draw the state of stress on a volume element (stress element) located at point E 5. Determine the principal stresses acting at point E by constructing Mohr's circle A 150 mm E 200 mm 30 mm 75 mm B F

Determine the normal strains at the point associated with the x and y axes. Determine the shear strain at the point associated with the x and y axes. Determine the normal stresses at the point associated with the x and y axes. Determine the shear stress at the point. Determine the normal stress that acts along an axis rotated at θ= 45° counterclockwise from the positive x-axis.

The state of stress at a point in a member is shown on the rectangular stress element; the magnitudes of the stresses are |σx|=66 MPa, |σy|=39 MPa|, and |τxy|=71 MPa. Using the stress-transformation equations, determine the state of stress on the inclined plane AB.