1. TA 101: Technical Arts 2015-16 II Dr. Prishati Raychowdhury Department of Civil Engineering IIT Kanpur Office: FB 330; Phone: 6692 E-mail: prishati@iitk.ac.inprishati@iitk.ac.in

2. Space Geometry-II Lecture 17

3. Review How to find the TRUE LENGTH of a Line? 1)Direct method 2)Rotation method 3)Auxiliary plane method

4. Finding True Length of a Line 1)Direct Method X Z X Y TL X Z X Y

5. Finding True Length of a Line 2)Method of Rotation X Z X Y TL X Z X Y

6. d1d1 d2d2 d1d1 d2d2 A BABA Auxiliary Plane Method Auxiliary plane (A) H F TRUE LENGTH (TL) AHAH BHBH A B BABA AFAF BFBF F P A H A d1d1 d2d2 d1d1 d2d2 AFAF BFBF AHAH BHBH H

7. Auxiliary Plane Concept F H bHbH bFbF aHaH aFaF TL H a A1 b A1 A1 A2 A1 a A2, b A2 PV of AB dAdA dBdB dAdA dBdB d1 A d1 B d1 A= d1 B Find TL and PV of line AB

8. Auxiliary Plane Concept H F P BHBH AHAH BFBF AFAF APAP BPBP A A1 B A1 F A1 A A2,B A2 TL A1 A2 PV of AB dAdA dBdB dAdA dBdB dAdA dBdB d1 A d1 B d1 A= d1 B Find TL and PV of line AB

9. Important Observations: Planes A B C A B C A B C A B C AB C ABC A B C A B C A B C EV TS EV TS EV Note: True Shape of a plane is available when line of sight is perpendicular to the EV

10. Important Observations: Planes A B C A B C A B C True Shape? A Note that in this scenario, True Shapes are not projected in any other principal planes EV of plane ABC

11. Important Observations: Planes A B C A B C B C True Shape? A This is an Oblique Plane: Neither parallel nor perpendicular to any of the principal planes This is the most general case of a plane

12. TL H V EV H A1 PV Note: If one sees any line of the plane in PV, the plane will be in EV Find EV of plane ABC

13. TL H V EV H A1 PV A1A2 TRUE SHAPE Note: True Shape of a plane is available when line of sight is perpendicular to the EV Find TRUE SHAPE of plane ABC

14. TL H V V A1 PV EV A1 A2 TS Projecting from Front View

15. Comparing Shapes: Projections from Top and Front Views TL H V V A1 PV EV A1 A2 TS

16. Mid Semester Exam Performance Total Marks = 50 Highest = 49 (4 students got this) Mean = 25.97 Standard Deviation = 12 Total no of students = 418 Section-wise mean = A123.30 A227.22 A325.09 A429.17 A530.75 A623.86 A724.47 A827.04 A925.72 A1026.80 A1123.60 A1225.09

17. Frequency Distribution of Mid Sem Marks Marks No of students

18. Mid Semester Exam Solutions Q1. Drawing ellipse using conjugate diameter method (10 Marks) Grading Policy: [1] Wrong Method (-6 marks), grading has been done out of 4 marks [2] Deduction of 1, 2, 3 or more marks depending on (a) Neatness (b) If the object lines and the construction lines are not distinguishable (c) Only a few number of points taken to draw the ellipse, resulting improper ellipse (d) If the object line is not a single line (or a smooth curve) etc. Note: Set B has different dimensions of ellipse, method remains same

19. Mid Semester Exam Solutions Q2. Orthographic Views with dimensions (15 Marks) Grading Policy: [1] Correctly making 2 views = 10 marks; and optimal dimensioning = 5 marks. [2] Deduction of 1, 2, 3 or more marks depending on the number of object/hidden lines missing from the views. Similarly, 1, 2, or more marks are deducted for number of missing dimensions and/or redundant dimensions. Note: Front and Profile views are altered in set B

20. Mid Semester Exam Solutions Q3. Isometric Projection (15 Marks) Grading Policy: (1) If isometric drawing is drawn instead of isometric projection, 5 marks are deducted. (2) If the wedges are not shown, 2 marks are deducted ( 1 mark for each wedge). (3) If slot is not shown, 2 marks are deducted. (4) Correct representation of top triangular cut out along with the rectangle carries 2.5 marks. (5) Correct representation of side triangular cut out along with the rectangle carries 2.5 marks. (6) Correct representation of object lines carries 1 mark. (7) If the oblique (cavalier or cabinet) view is presented, 7.5 marks are deducted and the grading is done out of 7.5 marks. Note: Object remains same in set A and set B

21. Mid Semester Exam Solutions Q4. Missing line, missing views (10 Marks) Grading Policy: [1] 5 marks for showing the missing lines and 5 marks for the free hand sketch (Total 10) [2] Further, if they have partially completed the missing lines, then either 2 or 3 marks are deducted (out of 5). Deduction policy was made according to the lines they have missed or erroneously made. [3] In free hand sketch, marks are deducted for drawing hidden lines in views, object lines which cannot be seen etc. 1 or 2 marks are deducted according to the severity of the mistake. [4] Marks are deducted for incorrect pictorial sketch, or if the pictorial sketch do not match with their completed orthographic solutions. Note: Views are only positioned differently (First or Third angle scheme) in set A and B, object remains the same

22. H F EDGE VIEW OF HORIZONTAL CEILING EDGE VIEW OF HORIZONTAL GROUND Y=RISE Y=RUN C D TL H Slope of a Line Slope = Rise/Run = (y/x) = tan (  H )  H is ‘slope angle’ of line CD Grade of line CD = 100 tan (  H ) %

23. F H AFAF BFBF AHAH BHBH A BABA H A Run (X) = 10 TL Slope of Line = Rise/Run = Y/X = - 0.5 = - 50% grade  H = -26 0 Slope of an Oblique Line Rise (Y) = -5 Find the slope of line AB

24. Slope of a Line Slope, slope angle, and grade of a line are considered ‘positive’ if the line rises upward as one travels along it from beginning to end Slope, slope angle, and grade of a line are considered ‘negative’ if one travels downward from beginning to end Correct slope of a line would be visible in which view? The view in which the line is seen in its TL

25. Bearing of a Line W N E S N 30 0 E N 60 0 W S 45 0 W C D B A

26. Bearing is used by engineers, pilots, and sailors on maps for specifying the alignment of a line in 2-D space (horizontal plane) Bearing of a line is its deviation (in terms of angle) from North or South The deviation angle is always an acute angle (less than 90 o ) Bearing can be seen in a horizontal view only Four special cases of bearing N0 o E - Due North N90 o E – Due East S0 o W – Due South S90 o W – Due West Bearing of a Line

27. W N E S B C A D N 30 0 N 225 0 N 300 0 Azimuth of a line is an alternative way to express the bearing of a line Azimuth is always read clockwise from the North arrow and uses only the letter N together with the clockwise angle Azimuth of a Line

28. Thank You