STRESSES IN INCLINED PLANES

1. UNIT – 3
ANALYSIS OF STRESSES IN TWO
DIMENSIONS

2. UNIT – 5
SYLLABUS
• Biaxial state of stress – thin cylinders and
shells – Deformation in Thin cylinders and
spherical shells. Thick Cylinders – Lame‘s
Equation – stresses on inclined planes –
Principal planes and stresses – Mohr‘s circle
for biaxial stress- Maximum shear stress.

3. Thin cylinder
The cylinder which have thickness is less than 1/10 to 1/20 of its
Diameter, that cylinder is called as thin cylinder.
The cylinder which have Thickness is more than 1/20 of its
diameter that Cylinder is called as thick Cylinder. Thin cylinder is
only resist to the internal Pressure.
Thick cylinder

5. Hoop stress
Hoop stress is the stress that occurs along the pipe's circumference
when pressure is applied. Hoop stress acts perpendicular to the axial
direction. Hoop stresses are tensile and generated to resist the bursting
effect that results from the application of pressure.

6. Longitudinal stress
• Stress acting in the direction parallel to the
longitudinal axis of the pipe's length due to internal
pressure is called longitudinal stress.

7. Formulas

8. Thin Spherical Shell

9. Thick cylinder
• A cylinder is considered to be 'thick' if the
ratio of the inner diameter to the thickness of
the walls is less than 20. ... In case of thin
cylinders, the hoop stress is determined by
assuming it to be uniform across the thickness
of the cylinder.

11. stresses on inclined planes

12. Mohr's circle method
• Mohr's circle is a graphical representation of
the transformation equations for plane stress
problems. It is useful in visualizing the
relationships between normal and shear
stresses acting on a stress element at any
desired orientation.