Yxy dy T Yxy - E;dx xp-

1. Element A is subjected to the stress state shown in the x-y plane 75 MPa (+x is to the right, +y is up). Use Mohr's Circle to solve the following problems. You MUST draw Mohr's Circle to get credit for these problems! 25 MPa 105 MPa (a) Determine the complete state of stress on the element in the x-y coordinate system. (b) Determine the state of stress if this element is rotated 25° (c) Determine the values of the principal stresses. (d) Determine the value of the maximum in-plane shear stress, Tmax in plans. (e) Determine the absolute maximum shear stress, Tmax abzolute (by drawing circles from each principal stress to the origin). Is Tmax abzoluts in the x-y plane (i.e., is Tmax absolute equal to Tmax, in-plane)? nswers: (a) ox = 105 MPa (T); oy = 75 MPa (T); Ty = +25 MPa; o; = Tx = Tyz = 0 (b) ox = 118.8 MPa (T); o, = 61.21 MPa (T); t = -4.579 MPa (c) 01.2 =119.2 MPa (T), 60.8 MPa (T) (d) Tmax in-plane = 29.15 MPa (e) Tmax absolute = 59.58 MPa; no, Tmax, absolute is not in the…

Question 2 In the below structure, the truss members stiffness matrix has been used for truss members and the beam stiffness matrix has been used for the rest. a) How many unknown displacements are in the displacement vector? b) How many displacements are in the displacement vector altogether? * J A

Solve using Mohr’s circle

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

T·r T (from torsion) = Tr4 J ="- (Solid rod) F Onormal = A o (from bending) M•y - (Solid rod) The solid rod shown in the figure below has diameter of 1.25 in. If it is subjected to the force of 60 lb, determine the state of stress at point A using the principle of superposition. Neglect the weight of the rod, and the stress due to the I %3D I 4 transverse shear force. 60 lb k-10 in.- 15 in. Front View -20 in. В

8 Expansion is an axial deformation. 9 True 10 False The coordinates of centroid locate the ge ometric center of the cross-section of the material.( True False Torsional stress is also known as bending stress.( True False

A differential element on the bracket is subjected to plane strain that has the following components: , strain at x = 250 x 10-6, strain at y = 300 x 10-6,  strain at x y= -500 x 10-6. Use the strain-transformation equations and determine the normal strain strain x' in the x' direction on an element oriented at an angle of 35°. Note, a positive angle is counter clockwise.

For the structure in the figure below , determine the correct answer. Roller- The structure is stable and determinate. The structure is statically unstable. The structure is geometrically unstable. The structure is stable and indeterminate.

2. From the given figure and data below. Determine the: a. P so that the structure is stable (in equilibrium) b. Draw the FBD of the member BC c. Reaction at A Weight of the member AB and BC = 50kg µ at C= 0.5 1.5 m 3m 1.5 m 30 30° 4, = 0.5