Handbook of Civil Engineering Calculations

EVALUATION OF PRINCIPAL STRESSES

The prism ABCD in Fig. 2 Ia is subjected to the normal and shearing stresses shown. Con-
struct Mohr's circle to determine the principal stresses at A, and locate the principal
planes.

Calculation Procedure:

1. Draw the lines representing the normal stresses (Fig. 21b)
   Through the origin O, draw a horizontal base line. Locate points E and F such that OE =
   8400 lb/in
   2
   (57,918.0 kPa) and OF = 2000 lb/in
   2
   (13,790.0 kPa). Since both normal
   stresses are tensile, E and F lie to the right of O. Note that the construction required here
   is the converse of that required in the previous calculation procedure.


2. Draw the lines representing the shearing stresses
   Construct the vertical lines EG and FH such that EG = 3600 lb/in^2 (24,822.0 kPa), and
   FH = -3600 lb/in^2 (-24,822.0 kPa).


3. Continue the construction
   Draw line GH to intersect the base line at C.


4. Construct Mohr's circle
   Draw a circle having GH as diameter, intersecting the base line at A and B. Then lines OA
   and OB represent the principal stresses.

(o) Stresses on prism

FIGURE 21

( c) Free -body diagram of AOJ

(b) Mohr's circle of stress