There are four different types of resultant loadings: Normal Force, Bending Moment, Magnetic force, and Torque. Normal Stress and Shear Stress are experienced on the same parallel planes. Shape change is associated with Normal Stress. The factor of safety (F.S.) is a ratio of the allowable load divided by the failure load. Stress is defined as the intensity of internal moments at a point.

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Learning Goal: Part A - Orientation of the planes of maximum and minimum normal stress To determine the in-plane principal stresses and maximum shear stress along with their orientations and the average normal stress for an element in a given state of plane stress. Determine the orientation of the planes of maximum and minimum normal stress, 0p1 and 0,2, respectively. Use the value for Op2 that is negative. Then use this value to determine the value of Op1 Express your answers to four significant figures separated by a comma. The element of material below is subjected to the state of stress shown, where a = 120.0 MPa, b = 62.00 MPa. and c = 12.00 MPa (Figure 1) • View Available Hint(s) Πν ΑΣφ vec Opl, Op2 = Submit Figure 1 of 1 Part B - In-plane principal stresses a Determine the in-plane principal stresses for the element (as oriented in Part A), and calculate oj and o2 such that they correspond with 0pl and 0p2 Express your answers to four significant figures separated by a comma. >…

Use Mohr circle

Displacement components at a point in a solid u(x, y,t) = 2y²x+2t v(x, y, t) = 8y'x + 5t2 w(x, y, t) = 3zy'x + 5xt² |3D a) the strain tensor, b) stress tensor c) Find out if the strain satisfies the fit equations?

Part B - The internal reaction at B Assume that the axial member is in equilibrium and the applied forces are an unknown load F₁. F = 5 kN. F₂ = 3 kN, and F₁ = 2 kN. Calculate the internal resultant normal force at section B. Express your answers to three significant figures in kN. ▸ View Available Hint(s) PB = Submit ΨΕ ΑΣΦΠ Part C - The internal reaction at D PD = Submit D] ΑΣΦΩΤ vec Assume that the axial member is in equilibrium and the applied forces are an unknown load F₁, F₂=5 kN. F₂ = 3 kN. and F₁ = 2 kN. Calculate the internal resultant normal force at section D. Express your answers to three significant figures in kN. ▸ View Available Hint(s) Part D - The average normal stress µA vec Value P * ? ? Units KN 2 ? Suppose the axial member has a circular cross section with a diameter of d = 16 cm at section B and a diameter of dp = 8 cm at section D. What is the average normal stress in the section with the maximum magnitude stress? Express your answer to three significant figures…

Transform the state of stress shown by rotating its orientation 50 degrees counterclockwise.  What is the normal stress (in MPa) on the face which originally had the 125 MPa tensile stress (i.e. the left and right of the element).  Make sure to enter a positive answer if it is in tension and a negative answer if it is in compression.

3 - A strain gauge is attached to the side of a beam, as shown by the cross-section view in the figure. When the beam is subjected to a specified uniform moment, the longitudinal strain measured by the gauge is -300μ. Plot the axial stress profile over the height of the cross- section. What is the magnitude of the moment that produced this strain gauge reading? Assume E = 75 GPa. 10↑ Strain gauge dimensions in mm 30 30 beamcross-section

Question 1: The general state of stress at a point is characterized by six independent normal and shear stress components which act on the faces of an element of material located at the point. Show a schematic view of the general state of stress. Using Mohr’s circle, determine the principal stresses of an element having σx = 45 MPa, σy = 55 MPa and ?xy = 25 MPa. Show them on a sketch of a properly oriented element. Using Mohr’s circle, determine the maximum and minimum shear stresses. Show them on a sketch of a properly oriented element. Determine the equivalent state of stress if the element is oriented 30º clockwise by using Mohr’s circle. Show them on a sketch of a properly oriented element.

Part C - Counterclockwise Rotation of a Stress Element Figure 5 of 6 The state of stress at a point in a member is shown on the rectangular stress element in (Figure 5) where the magnitudes of the stresses are |0z| = 13 ksi, Joy = 23 ksi, and |Tzy| = 12 ksi. Determine the state of stress on an element rotated 45° counterclockwise from the element shown. Express your answers, separated by commas, to three significant figures. • View Available Hint(s) Vol AEO I vec Or =, oy =, Tự'y = ksi, ksi, ksi Submit Pearson