24-01-2013, 01:50 PM
SECTIONS OF SOLIDS
[attachment=48296]
An object is difficult to visualize from its orthographic views if its internal structure is complicated.
In such a case, the concept of ‘sectioning the object’ helps to interpret and visualize the object easily.
The object is assumed to be cut by an imaginary plane to reveal internal details.
The imaginary plane which cuts the object is called the cutting plane (or section plane). The new imaginary face generated on the object is called the section.
Whenever a section plane cuts a solid, it intersects (and or coincides with) the edges of the solids.
The point at which the section plane intersects an edge of the solid is called the point of intersection (POI).
Our focus shall be on finding these points of intersection.
True Shape of a Section
A section will show its true shape when viewed in normal direction. Obviously, to find the true shape of a section, it must be projected on a plane parallel to the section plane.
For polyhedra, the true shape of the section depends on the number of POIs. The shape of the section will be a polygon of the sides equal to the number of POIs.
The true shape of the section of a sphere is always a circle.
The sections of prisms and pyramids are straight line segmented curves.
The sections of cylinders and cones will mostly have smooth curves.
SECTIONS OF CYLINDERS
Example 15.19 A cylinder with a 60 mm diameter and a 100 mm height stands on its base on the HP. It is cut by two section planes,
(i) an AIP inclined at 60° to the HP and intersecting an extreme generator at a point 36 mm from the base and,
(ii) an AVP inclined at 75° to the VP and 21 mm away from the axis of the cylinder.
Draw the sectional TV and sectional FV.
[attachment=48296]
An object is difficult to visualize from its orthographic views if its internal structure is complicated.
In such a case, the concept of ‘sectioning the object’ helps to interpret and visualize the object easily.
The object is assumed to be cut by an imaginary plane to reveal internal details.
The imaginary plane which cuts the object is called the cutting plane (or section plane). The new imaginary face generated on the object is called the section.
Whenever a section plane cuts a solid, it intersects (and or coincides with) the edges of the solids.
The point at which the section plane intersects an edge of the solid is called the point of intersection (POI).
Our focus shall be on finding these points of intersection.
True Shape of a Section
A section will show its true shape when viewed in normal direction. Obviously, to find the true shape of a section, it must be projected on a plane parallel to the section plane.
For polyhedra, the true shape of the section depends on the number of POIs. The shape of the section will be a polygon of the sides equal to the number of POIs.
The true shape of the section of a sphere is always a circle.
The sections of prisms and pyramids are straight line segmented curves.
The sections of cylinders and cones will mostly have smooth curves.
SECTIONS OF CYLINDERS
Example 15.19 A cylinder with a 60 mm diameter and a 100 mm height stands on its base on the HP. It is cut by two section planes,
(i) an AIP inclined at 60° to the HP and intersecting an extreme generator at a point 36 mm from the base and,
(ii) an AVP inclined at 75° to the VP and 21 mm away from the axis of the cylinder.
Draw the sectional TV and sectional FV.