REVIEW EXAM 1

1. As the y axis is the axis of symmetry, the centroid will lie on the y axis. Thus z _c = 0.

   Note

   1 point

   Equations (A.5) and (A.9) can be used to find the y coordinate of the centroid and the area moment of inertia.

   Calculation of centroid (Figure F.1).

   
   Figure F.1

   Note	1 point for each correct entry Total 8 points

   Section	Y ci (mm)	A i (mm 2)	Y ci A i (mm 3)
   1	30	60 10 = 600	18,000
   2	65	50 10 = 500	32,500
   Total		1100	50,500

   From Equation (A.5) we obtain

   
   

   Note	1 point for correct answer and units

   Calculation of area moment of inertia

   Section	d zi = Y c ? Y ci (mm)		I zizi + A i d 2 zi (mm 4)
   1	15.9	10 60 3/12 = 180 10 3	331.7 10 3
   2	19.1	50 10 3/12 = 4.2 10 3	186.6 10 3
   	1 point for each correct entry	2 points for each correct entry	1 point for each correct entry

   From Equation (A.9) we obtain

   
   

   Note	1 point for correct answer

   Note	1 point for correct units

2. We can replace each linear loading by an equivalent force, as shown in Figure A.8, then replace it by a single force. Using Figure F.2 we obtain

   
   

   Note