An element on the top surface of the fuel tanker in Problem 7.2-1 is in biaxial stress and is subjected to stresses   x = - 48 MPa and   y = 19 MPa, as shown in the figure. Using Mohr’s circle,...

An element on the top surface of the fuel tanker in Problem 7.2-1 is in biaxial stress and is subjected to stresses
_x
= - 48 MPa and
_y
= 19 MPa, as shown in the figure. Using Mohr’s circle, determine the following.

(a) The stresses acting on an element oriented at a counterclockwise angle
 = 25⁰
from the x axis.

(b) The maximum shear stresses and associated normal stresses.

Show all results on sketches of properly oriented elements.

Problem 7.2-1

The stresses on the bottom surface of a fuel tanker (figure part a) are known to be

_x
=  50 MPa,

_y
= 8 MPa , and t
_xy
= 6.5 MPa (figure part b).

Determine the stresses acting on an element oriented at an angle
 = 52⁰
from the x axis, where the angle
 is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle
.