In an elastic body without any body force, the Airy's stress function determined as: $ = x*y + 4x²y3 – y5 i) Check whether this function is satisfying Biharmonic equation or not. ii) Determine the stress components.

A steel rectangular block is subjected to a uniform stress of o = 150 MPa acting on all faces. The dimensions of the block are as follows: Lx=100 mm,L_y=30 mm,L_z=40 mm. Determine the change in length along the x-axis. Use E = 200 GPa and v = 0.3. Note that e_0=- o/E(1+2v). (A) -0.03 mm B) -0.009 mm C) -0.015 mm D -0.012 mm

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Remember it has to be in meters for part B and C please they are linked

Two wooden studs with cross-sectional dimensions 45×145 mm2 are glued together to form a beam with a T-sectionaccording to the figure on the right and loaded according to the figure on the left. The beam is loaded in its rigiddirection.a) Calculate the moment of inertia of the cross-section about the centroid axis (z-axis).b) Calculate the maximum normal stress in the beam.c) Sketch the normal stress distribution over the most loaded cross-section of the beam. All calculations must be clear and handwritten, draw and check so that the answers are correct

Q3 / An element in plane stress at the surface of a large machine is subjected to stresses shown below. Using Mohr's circle determine the following quantities (a) the principal stresses and their directions and (b) the maximum shearing stresses and the directions of the planes on which they occur. 100 MPa 50 MPa 75 MPa 75 MPa 50 MPa 100 MPa

Example: The state of plane stress at a point is represented by the stress element below. Draw the Mohr's circle, determine the principal stresses and the maximum shear stresses, and draw the corresponding stress elements. 50 MPa B0 MPa O MPa 25 MPa 50 MPa

The state of stress at a point in a member is shown in A 0x' = 60° σ y Tx'y' B x on the element. Assume o and oy act in the directions shown and have magnitudes of o = 770 psi and oy = 490 psi . Solve the problem using the method of equilibrium. Part A = Determine the normal stress component acting on the inclined plane AB. O Express your answer in pounds per square inch to three significant figures. ANSWER: X psi Tap image to zoom Part B Determine the shear stress component acting on the inclined plane AB. Express your answer in pounds per square inch to three significant figures. ANSWER: psi

The stresses shown act at a point on the free surface of a machine component. Normal and shear stress magnitude acting on horizontal and veritcal planes at the point are Sx= 12.7 ksi, Sy= 1.7 ksi, Sxy= 5.8 ksi. Assume beta= 34 degrees. Determine the normal stresses and shear stress

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