Solve parts (a) to (c) using transformation equations only (not Mohr's circle), and show the complete state of stress with the appropriate stress element properly oriented relative to the given xy coordinate system. Given the state of plane stress shown, (a) determine the state of stress for an element oriented 20° clockwise relative to the given xy coordinate system. (b) determine the state of stress for the element containing the principal stresses. (c) determine the state of stress for the element containing the maximum in- plane shear stresses.

What causes the localized buckling of the beam's flanges?

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The stresses acting on element A in the web of a train rail are found to be ‘X (MPa)’tension in the horizontal x-direction and ‘Y (MPa)’ compression in the verticaly-direction. Also, shear stresses of magnitude ‘S (MPa)’ act in the directions shown inthe figure.a) Draw Mohr’s circle for the state of stress.b) Determine the stresses (σx', σy' and τxy') acting on an element oriented at an angle‘D’ from the horizontal. Show these stresses on a sketch of an elementoriented at this angle (X (MPa)=75) ( Y (MPa)=90) ( S (MPa)=40) ( D ( ˚ )=-10)   Note: If the angle D is positive, then the shear stress is in the direction shown onthe unit element figure; if it is a minus sign, then the shear stress is in theopposite direction shown on the unit element figure.

The state of stress at a point in a soil beneath a level ground surface consists of a major principal stress of 70 kPa and a minor principal stress of 25 kPa. The major principal stress acts in the vertical direction. (a) Draw the Mohr's circle of stress and show the pole point (origin of planes). (b) Determine the maximum shear stress and calculate the orientation angle (relative to horizontal) of the plane of positive maximum shear stress. (c) Determine the normal stress and shear stress on a plane that makes an angle of -20° (i.e., 20° clockwise) relative to the horizontal plane.

1. A loaded bicycle pedal crank is shown below. q 750N (2 direction) 72/ A @ Top 8 yo B@ Top d = 15 mm x₁ = 125 mm x2 = 24 mm y₁ = 60 mm у2=X2 a. Sketch elements A and B and show the stress states. Clearly label the coordinate axes on the elements. Make sure you calculate the normal (o) and shear stresses (T). Do not neglect Tv. Find the principal stresses for each element using Mohr's Circle. b.

Determine (a) the principal stresses, and (b) the maximum in-plane shear stress and the associated average normal stress. Also, for each case, determine the corresponding orientation of the element with respect to the element shown and sketch the results on the element. INSTRUCTIONS: For full credit (10 points), must use stress transformation formulas and submit the pdf of your work. Also, in the space provided below, enter the value of the maximum in-plane shear stress (in MPa) using three significant digits (5 points). 50 MPa 140 MPa

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