For the objects shown on the left below, circle the letters corresponding to all possible cross-sections that could be obtained by slicing it with an appropriate cutting plane. There could be more than one correct answer. 1. 2. A A B B C HC D 0

Determine the x and y-coordinate of the centroid shown below.

The figure shows a cutaway view of an assembly in which a solid bronze [G = 6,500 ksi] rod (1) is fitted inside of an aluminum alloy [G = 4,000 ksi] tube (2).  The tube is attached to a fixed plate at C, and both the rod and the tube are welded to a rigid end plate at A.  The rod diameter is d1 = 2.05 in.  The outside diameter of the tube is D2 = 2.8 in. and its wall thickness is t2 = 0.110 in.  Overall dimensions of the assembly are a = 55 in. and b = 11 in.  The allowable shear stresses for the bronze and aluminum materials are 10800 psi and 7800 psi, respectively.  Further, the rotation angle of end B must be limited to a magnitude of 4.8°.  Based on these constraints, what is the maximum torque TB that can be applied at end B?

• The origin of the "standard coordinate system" shall be located at the bottom-left-hand corner of this cross-section. NOTE: Submitted responses shall be to 4 significant figures. Do NOT use scientific notation. Find: 1. The net area (area of the material) is in. 2. The x-coordinate of the centroid is. in. 3. The y-coordinate of the centroid is_ in. 4. The Area Moment of Inertia about the x-axis is_in'. 5. The Area Moment of Inertia about the centroidal x-axis is int. 6. The Radius of Gyration about the x-axis is 7. The Radius of Gyration about the centroidal x-axis is _in. in. 2 in. 6 in. 1 in. 4 in. 1 in.

The figure shows a cutaway view of an assembly in which a solid bronze [G= 6,500 ksi] rod (1) is fitted inside of an aluminum alloy [G = 4,000 ksi] tube (2). The tube is attached to a fixed plate at C, and both the rod and the tube are welded to a rigid end plate at A. The rod diameter is d₁ = 1.15 in. The outside diameter of the tube is D₂ = 3.4 in. and its wall thickness is t₂ = 0.130 in. Overall dimensions of the assembly are a = 50 in. and b = 14 in. The allowable shear stresses for the bronze and aluminum materials are 10600 psi and 7600 psi, respectively. Further, the rotation angle of end B must be limited to a magnitude of 4.3°. Based on these constraints, what is the maximum torque Te that can be applied at end B? Fixed End plate 12 plate TB Rod (1) A Tube (2) W a D2 Answer: TB = lb-in b B

Find the centroid of the figure below.

While cutting a piece of paper, a person exerts the two indicated forces on a paper cutter. Reduce the two forces to an equivalent force-couple system at corner O and then specify the coordinates of the point P in the x-y plane through which the resultant of the two forces passes. The cutting surface is 28" x 28". 30 lb 13" A 4" 5 lb 1"

The figure shows a cutaway view of an assembly in which a solid bronze [G= 6,500 ksi] rod (1) is fitted inside of an aluminum alloy [G = 4,000 ksi] tube (2). The tube is attached to a fixed plate at C, and both the rod and the tube are welded to a rigid end plate at A. The rod diameter is d₁ = 1.55 in. The outside diameter of the tube is D₂ = 2.8 in. and its wall thickness is t₂ = 0.115 in. Overall dimensions of the assembly are a = 35 in. and b = 11 in. The allowable shear stresses for the bronze and aluminum materials are 9800 psi and 8500 psi, respectively. Further, the rotation angle of end B must be limited to a magnitude of 4.2°. Based on these constraints, what is the maximum torque Tg that can be applied at end B? Fixed End plate plate di TB Rod (1) D₂ Answer: TB = A Tube (2) a lb-in b B

Plate A is situated in a coordinate plane as shown. The diameter of the plate is 20mm while its centroid is located at (90mm, 8mm). The radius of gyration of B with respect to the x-axis is (in 2 decimal places): kx || = +y mm B +x

While cutting a piece of paper, a person exerts the two indicated forces on a paper cutter. Reduce the two forces to an equivalent force-couple system at corner O and then specify the coordinates of the point P in the x-y plane through which the resultant of the two forces passes. The cutting surface is 30" x 30". 10 lb 20 lb 14" 10" x. 2" 6" Part 1 There are 2 distinct questions here. We will solve the first question now. Question 1: Replace the two forces shown by an equivalent force-couple system at point 0. Find the force part of the force-couple system. Answer: F = i + j+ k) lb