6. Section of solids and development of surfaces.ppt
- 1. ENGINEERING DRAWING Section of Solids, Development & Intersections
- 2. 1. SECTIONS OF SOLIDS 2. DEVELOPMENT 3. INTERSECTIONS ENGINEERING APPLICATIONS OF THE PRINCIPLES OF PROJECTIONS OF SOLIDS STUDY CAREFULLY THE ILLUSTRATIONS GIVEN ON NEXT SIX PAGES !
- 3. SECTIONING A SOLID. An object ( here a solid ) is cut by some imaginary cutting plane to understand internal details of that object. The action of cutting is called SECTIONING a solid & The plane of cutting is called SECTION PLANE. Two cutting actions means section planes are recommended. A) Section Plane perpendicular to Vp and inclined to Hp. ( This is a definition of an Aux. Inclined Plane i.e. A.I.P.) NOTE:- This section plane appears as a straight line in FV. B) Section Plane perpendicular to Hp and inclined to Vp. ( This is a definition of an Aux. Vertical Plane i.e. A.V.P.) NOTE:- This section plane appears as a straight line in TV. Remember:- 1. After launching a section plane either in FV or TV, the part towards observer is assumed to be removed. 2. As far as possible the smaller part is assumed to be removed. OBSERVER ASSUME UPPER PART REMOVED OBSERVER ASSUME LOWER PART REMOVED (A) (B)
- 4. ILLUSTRATION SHOWING IMPORTANT TERMS IN SECTIONING. x y TRUE SHAPE Of SECTION SECTION PLANE SECTION LINES (450 to XY) Apparent Shape of section SECTIONAL T.V. For TV
- 5. Section Plane Through Apex Section Plane Through Generators Section Plane Parallel to end generator. Section Plane Parallel to Axis. Triangle Ellipse Hyperbola Ellipse Cylinder through generators. Sq. Pyramid through all slant edges Trapezium Typical Section Planes & Typical Shapes Of Sections.
- 6. DEVELOPMENT OF SURFACES OF SOLIDS. MEANING:- ASSUME OBJECT HOLLOW AND MADE-UP OF THIN SHEET. CUT OPEN IT FROM ONE SIDE AND UNFOLD THE SHEET COMPLETELY. THEN THE SHAPE OF THAT UNFOLDED SHEET IS CALLED DEVELOPMENT OF LATERLAL SUEFACES OF THAT OBJECT OR SOLID. LATERLAL SURFACE IS THE SURFACE EXCLUDING SOLID’S TOP & BASE. ENGINEERING APLICATION: THERE ARE SO MANY PRODUCTS OR OBJECTS WHICH ARE DIFFICULT TO MANUFACTURE BY CONVENTIONAL MANUFACTURING PROCESSES, BECAUSE OF THEIR SHAPES AND SIZES. THOSE ARE FABRICATED IN SHEET METAL INDUSTRY BY USING DEVELOPMENT TECHNIQUE. THERE IS A VAST RANGE OF SUCH OBJECTS. EXAMPLES:- Boiler Shells & chimneys, Pressure Vessels, Trays, Boxes & Cartons, Feeding Hoppers, Large Pipe sections, Body & Parts of automotives, Ships, Aeroplanes and many more. WHAT IS OUR OBJECTIVE IN THIS TOPIC ? To learn methods of development of surfaces of different solids, their sections and frustums. 1. Development is different drawing than PROJECTIONS. 2. It is a shape showing AREA, means it’s a 2-D plain drawing. 3. Hence all dimensions of it must be TRUE dimensions. 4. As it is representing shape of an un-folded sheet, no edges can remain hidden And hence DOTTED LINES are never shown on development. But before going ahead, note following Important points. Study illustrations given on next page carefully.
- 7. D H D S S H = R L 3600 R=Base circle radius. L=Slant height. L= Slant edge. S = Edge of base H= Height S = Edge of base H= Height D= base diameter Development of lateral surfaces of different solids. (Lateral surface is the surface excluding top & base) Prisms: No.of Rectangles Cylinder: A Rectangle Cone: (Sector of circle) Pyramids: (No.of triangles) Tetrahedron: Four Equilateral Triangles All sides equal in length Cube: Six Squares.
- 8. = R L 3600 R= Base circle radius of cone L= Slant height of cone L1 = Slant height of cut part. Base side Top side L= Slant edge of pyramid L1 = Slant edge of cut part. DEVELOPMENT OF FRUSTUM OF CONE DEVELOPMENT OF FRUSTUM OF SQUARE PYRAMID STUDY NEXT 13 PROBLEMS OF SECTIONS & DEVELOPMENT FRUSTUMS
- 9. X Y X1 Y1 A B C E D a e d b c A B C D E A DEVELOPMENT a” b” c” d” e” Problem 1: A pentagonal prism , 30 mm base side & 50 mm axis is standing on Hp on it’s base whose one side is perpendicular to Vp. It is cut by a section plane 450 inclined to Hp, through mid point of axis. Draw Fv, sec.Tv & sec. Side view. Also draw true shape of section and Development of surface of remaining solid. Solution Steps:for sectional views: Draw three views of standing prism. Locate sec.plane in Fv as described. Project points where edges are getting Cut on Tv & Sv as shown in illustration. Join those points in sequence and show Section lines in it. Make remaining part of solid dark. For True Shape: Draw x1y1 // to sec. plane Draw projectors on it from cut points. Mark distances of points of Sectioned part from Tv, on above projectors from x1y1 and join in sequence. Draw section lines in it. It is required true shape. For Development: Draw development of entire solid. Name from cut-open edge I.e. A. in sequence as shown. Mark the cut points on respective edges. Join them in sequence in st. lines. Make existing parts dev.dark.
- 10. Y h a b c d e g f X a’ b’ d’ e’ c’ g’ f’ h’ o’ X1 Y1 g” h”f” a”e” b”d” c” A B C D E F A G H SECTIONAL T.V SECTIONAL S.V DEVELOPMENT Problem 2: A cone, 50 mm base diameter and 70 mm axis is standing on it’s base on Hp. It cut by a section plane 450 inclined to Hp through base end of end generator.Draw projections, sectional views, true shape of section and development of surfaces of remaining solid. Solution Steps:for sectional views: Draw three views of standing cone. Locate sec.plane in Fv as described. Project points where generators are getting Cut on Tv & Sv as shown in illustration.Join those points in sequence and show Section lines in it. Make remaining part of solid dark. For True Shape: Draw x1y1 // to sec. plane Draw projectors on it from cut points. Mark distances of points of Sectioned part from Tv, on above projectors from x1y1 and join in sequence. Draw section lines in it. It is required true shape. For Development: Draw development of entire solid. Name from cut-open base point i.e. A, in sequence as shown.Mark the cut points on respective edges. Join them in sequence in curvature. Make existing parts dev.dark.
- 11. Problem 3: A square pyramid, 30mm long base sides and 50 mm long axis is resting on Hp on one corner of base with a slant edge 600 inclined to Hp while it’s Axis is parallel to Vp. It is cut by a horizontal section plane. Draw it’s projections And development. a’ b’ c’ d’ a b c d o o’ a1 b1 d1 o1 600 X Y a’ b’ c’ d’ o’ 1’’ 3’ 2’ 1 2 3 Base side Development O A A D C B Follow similar solution steps for Sec.views – True shape – Development as per previous problem!
- 12. Problem 4: A triangular pyramid of 30 mm long base side and 50 mm long axis Is placed on Hp on one of it’s edges of base such that it’s opposite base corner is 25 mm above Hp. Draw it’s projections when it’s Axis is parallel to Vp. Draw true shape of section and development. a b c o a’ b’ c’ o’ 25mm a1 b1 c1 o1 X Y a’ b’ c’ o’ 1’’ 3’ 2’ 1 3 2 1 3 2 SECTION PLANE // TO AXIS TRUE SHAPE OF SECTION SECTIONAL TV FV O C B A A Base side Development Follow similar solution steps for Sec.views – True shape – Development as per previous problem!
- 13. Problem 5 A pentagonal prism of 30 mm long base edges and 55 mm long axis is standing on Hp With one base side perpendicular to Vp. Draw it’s projections. It is cut by a section plane, 450 inclined to Vp & which is 10 mm away from axis. Draw sectional Fv, Side view and development of remaining prism. a’ b’ c’ d’ a b c d e e’ 1’ 2’ 3’ 4’ 5’ X Y 20 D 450 a’’ b’’ c’’ d’’ e’’ 5’’ 1’’ 2’’ 3’’ 4’’ Section plane 450 inclined to Vp. E A B C D A 1 2 3 4 5 1 Development Longer Edge Base Edge
- 14. X Y e’ a’ b’ d’ c’ g’ f’ h’ o’ o’ Problem 6: A cone 40mm diameter and 50 mm axis is resting on one generator on Hp( lying on Hp) which is // to Vp.. Draw it’s projections.It is cut by a horizontal section plane through it’s base center. Draw sectional TV, development of the surface of the remaining part of cone. A B C D E F A G H O a1 h1 g1 f1 e1 d1 c1 b1 o1 SECTIONAL T.V DEVELOPMENT (SHOWING TRUE SHAPE OF SECTION) HORIZONTAL SECTION PLANE h a b c d e g f O Follow similar solution steps for Sec.views - True shape – Development as per previous problem! Cone Lying on Hp. Cone standing on Hp.
- 15. A.V.P300 inclined to Vp Through mid-point of axis. X Y 1 2 3 4 5 6 7 8 b’ f’ a’ e’ c’ d’ a b c d e f a1 d1 b1 e1 c1 f1 X1 Y1 AS SECTION PLANE IS IN T.V., CUT OPEN FROM BOUNDRY EDGE C1 FOR DEVELOPMENT. C D E F A B C DEVELOPMENT SECTIONAL F.V. Problem 7: A hexagonal prism. 30 mm base side & 55 mm axis is lying on Hp on it’s rect.face with axis // to Vp. It is cut by a section plane normal to Hp and 300 inclined to Vp bisecting axis. Draw sec. Views, true shape & development. Use similar steps for sec.views & true shape. NOTE: for development, always cut open object from From an edge in the boundary of the view in which sec.plane appears as a line. Here it is Tv and in boundary, there is c1 edge.Hence it is opened from c and named C,D,E,F,A,B,C. Note the steps to locate Points 1, 2 , 5, 6 in sec.Fv: Those are transferred to 1st TV, then to 1st Fv and Then on 2nd Fv. Prism Lying on Hp. Prism standing on Hp.
- 16. a c b d a’ b’ c’ o’ d’ 3 2 1 3’ 4 2’ 4’ 1’ a’ b’ d’ c’ 1’’ 4’ 3’ 2’ 1 3 4 2 a1 c1 b1 d1 Problem 8: A square pyramid of 30mm long base sides and 50 mm long axis is standing on it’s base on Hp. It is cut by a section plane through mid point of axs, 300 inclined to Hp .Draw it’s projections. Draw it’s Fv and Tv when it rests on Hp on it’s cut face on Hp with it’s axis is parallel to Vp. a’’ b’’ c’’ d’’ 4’’ 3’’ 2’’ 1’’
- 17. Thank you Source: Engineering Graphics Communication, Gary R. Betoline, IRWIN Graphics Series Engineering Drawing: plane and Solid Geometry, N.D. Bhatt, Charotar Publishing House, Anand