CEE 220

Quiz  6 - Solution

1.  Given s_x = -2 ksi, s_y = 10, t_xy = 8,

a)  Draw the Mohr circle to approximate scale, and label points X and Y, and the center C.

b) What is the radius of the circle?

c) What are the principle stresses?

d) What is the angle that the major principal axis makes with the x axis? Show the relative orientation on a sketch, or on the Mohr circle.

e) Show on a sketch the stresses acting on an element oriented at 45^o to the principal axes.

b) R is hypotenuse of (6,8,10) triangle.  R = 10 ksi.

c) abscissas of the extremities of the horizontal diameter: 14 and -6 ksi.

d) tanq_p = 8/4 = 2, q_p = 63.43 deg., as shown in figure.

e)

2. The column has a square cross section of side a = 12 in.  A force P = 100 k is applied at the top at a distance e = 2 inch from the centroid, as shown in projection in the bottom figure.  Determine the maximum normal stress at the base of the column, and indicate whether tensile or compressive and where it occurs.

Axial force:  N = - P = - 100k (compressive )

Bending moment:  M_z = - Pe = -100(2) =  -200 k-in 

A = 12(12) = 144 in²

I = 12(12)³/12 =  1728 in⁴

Maximum stress is compressive, and occurs along AB:

|s_B| = P/A + Mc/I = 100/144 + 200(6)/1728 = 1.390 ksi (compressive)

or

s_B = N/A - M_zy/I = -100/144 + 200(-6)/1728 = -1.390 ksi