Jitendra Shah Feb 2012 Todays Class Sections of prisms Sections - - PowerPoint PPT Presentation

Jitendra Shah Feb 2012

Today’s Class

Sections of prisms Sections of pyramids Sections of cylinders Sections of cones Sections of spheres

Because hidden lines are not enough to visualize internal details, often. By imagining removal of the portion between viewer and the cutting plane, the details can be better visualized (new terms: cutting plane, section plane) When projected on a plane parallel to section plane, the true shape of section is visible.

How to show section planes

In the view where section plane is perpendicular to projection plane, you will see a line The way to show section plane is as in next figures : Chain , thin, thick at ends and also thick at change in directions

When section planes are inclined to ref planes,

projection on auxiliary planes needed to see true view

How to show section lines

Typically at 45°. But when different materials and different parts variety of styles ( thickness and angles) used to differentiate parts

• r materials in section view of an assembly.

Sections of prisms 1.section plane parallel to V.P.

• Ex. A cube of 35 mm long edges resting on the H.P. on one of its

faces with a vertical face inclined at 300 to the V.P. it is cut by a section plane parallel to the V.P. And at a distance of 10 mm from the axis of cube , on the side away from VP. Draw sectional front view and top view

300 X Y

1.section plane parallel to V.P.

Solution – 1. Draw projections of cube in F.V. and T.V.

a b c1 d e f g1 h a1 b1 d1 f 1 h1 e 1 g c

35 mm

Sections of prisms 1.section plane parallel to V.P.

• 2. Draw the section plane HT 10 mm from axis

X Y 300 H T 10mm O

a b c1 d e f g1 h a1 b1 d1 f 1 h1 e 1 g c

35mm

Sections of prisms 1.section plane parallel to V.P.

• 3. Project the points cut by plane and draw Section

lines

X Y 300 O 10 mm H T

a b c1 d e f g1 h a1 b1 d1 f 1 h1 e 1 g c 11 2 3 4 1 21 31 41

In a section view of machine elements no edges or dotted lines should be shown. The dotted line in image on left is a mistake

• Ex. Same problem but section plane inclined 600 to V.P.

1.Draw projections in F.V. & T.V.

• 2. Draw the section plane HT 10 mm from axis inclined at 600 to V.P.

Sections of prisms 2.section plane perpendicular to H.P. & inclined to V.P.

300 X O

a b c1 d e f g1 h a1 b1 d1 f 1 h1 e 1 g c

H Y

• 1. Draw projection of cube

in TV and FV with its one face inclined at angle 30 degree to VP

Section of prisms

300 X O

a b c1 d e f g1 h a1 b1 d1 f 1 h1 e 1 g c

10 mm H T Y 600

• 2. Draw a section plane

inclined at 60 degree to VP and 10 mm away from centre of cube

Section of prisms

Sections of prisms 2.section plane perpendicular to H.P. & inclined to V.P.

300 X O

a b c1 d e f g1 h a1 b1 d1 f 1 h1 e 1 g c

10 mm H X1 Y 600 Y1

• 3. Draw new reference line

X1Y1 parallel to HT (auxiliary vertical plane ) Error in graphics as shown here Do Not draw all edges as final lines. Keep the boundaries as construction lines. After sectioning , the removed edges will remain

• nly as construction lines.

Sections of prisms 2.section plane perpendicular to H.P. & inclined to V.P.

300 X O

a b c1 d e f g1 h a1 b1 d1 f 1 h1 e 1 g c

10 mm H X1 Y

11 2 3 4 1 21 31 41 11

1

211 311 411

600 Y1

• 4. Draw the projections of

section on the new plane(to get true shape) & on the F.V.

• 5. Draw section lines

Sections of pyramids

• Ex. A square pyramid , base 40 mm side & axis 65 mm long has

its base on H.P. and all the edges of the base equally inclined to the V.P. It is cut by a section plane, perpendicular to the V.P. , inclined at 450 to the H.P. & bisecting the axis . Draw its sectional top view , sectional side view & true shape of the section

Sections of pyramids

Solution

• 1. draw the projections of pyramid in required position

Y

a1 b1 c1 a b c d

• 1

65mm 40mm x

Sections of pyramids

2.Draw line V-T 450 to X-Y bisecting the axis & then all sectional views.

X Y

a1 b1 c1 a b c d

• 1

4 5

V T

11 21 31 41 2 3 4 1 a b d 2 3 4 1

32.5mm

Sections of pyramids

3.Draw line V-T 450 to X-Y bisecting the axis & then all sectional views and true shape

X Y

a1 b1 c1 a b c d

• 1

4 5

V T

11 21 31 41 21 2 3 4 1

True shape

a b d 2 3 4 1 2 3 4 1

The width of true shape (2-4) can be measured in Side view and placed in true shape

Sections of cylinders

Ex. A cylinder of 40 mm diameter, 60 mm height & having its

axis vertical , is cut by a section plane ,perpendicular to the V.P. , inclined at 450 to the H.P. and intersecting the axis 32 mm above the base. Draw its front view ,sectional top view ,sectional side view & true shape of the section.

Sections of cylinders

Solution-

• 1. Draw projections in F.V. ,T.V. and L.H.S.V

x Y 60mm 40 mm Centre lines are a MUST In case of bodies of Revolution

Sections of cylinders

2.Draw sectional line VT .

4 5

V T

a c d b c1 d1 b1 g

X Y 32mm 40 mm

Sections of cylinders

• 3. Complete the sectional views (the projections of section of

circular should appear as ellipse in side view , right? It looks like a circle. Is there an error ? )

4 5

V T

b1

g1

c11 d1 e1 b11 c1 d11 e11 a c d b a c d b c1 d1 b1 c1 d1 b1 a1 f11 f1 g g

X Y 32mm

Sections of cylinders

• 4. Draw true shape in auxiliary plane

4 5

V T

a c d b c1 d1 b1 g a c d b c1 d1 b1 g b1

g1

d1 e1 b11 c1 d11 e11 a1 f1 c11 f11 a c d b c1 d1 b1 g

X Y True shape Lines of symmetry MUST be shown For circles and Elipses The chain lines must Extend beyond the body

Sections of cones

• Ex. A cone , base 75 mm diameter & axis 80 mm long is resting
• n its base on the H.P. it is cut by a section plane perpendicular

to the V.P., inclined at 450 to the H.P. & cutting the axis at a point 35 mm from the apex . Draw its F.V., sectional T.V. ,sectional side view & true shape of the section

Sections of cones

Solution-

• 1. Draw projections in F.V. ,T.V. and L.H.S.V

X Y 80m m

Sections of cones

2.Draw sectional line VT & complete the sectional views (How do you get d1 and d in top view. Since the projector and generator coincide? In every other case, you can get an intersection between projector and generator. Use circle method)

X Y

4 5

T

a1

V

a c d b c1 d1 b1 e1 f e f1g a c d b c1 d1 b1 e1 f1 e f g

Sections of cones

• 3. Draw true shape in auxiliary plane

X Y

4 5

T

a1

V

a c d b c1 d1 b1 e1 f e f1g a c d b c1 d1 b1 e1 f1 e f g a c d b c1 d1 b1 e f1 g e1 f

A cone , base 75mm dia, and axis 80 mm long is resting on its base on HP is cut by a plane perpendicular to VP, and parallel to and 12 mm away from one of its end generator. Draw its front view, sectional top view, true shape of the section (ref problem 14-24 , 14-25, N D Bhatt )

Draw cone and draw a section plane in FV Find the position of points on the section boundary and width of section at each point. How? Generator Method : draw generators and project intersection . Use rotation of the body to get

• therwise difficult-to-locate points like on

central generator Circle Method : e.g. In case of section plane parallel to base. You can get the width at any point by projecting on a circle in top view

Name the centre as O in TV and O' in FV Divide base circle (TV) in 12 parts. Draw generators. Number points from 1 to 12 in TV. Project the points on base line in FV and number them as 1' to 12' in FV Draw O'2' to cut section line at points namele b' and so on. Project these (b', c'..) on corresponding lines in TV. Symmetry around axis parallel to xy line. This gives section in TV How will you project the point where axis of the cone cuts the section line in FV (hint: use turn the cone, use end generator, drop projector, draw arc ...) True shape: ? Sectional View : ?

Thank You