STRENGTH OF MATERIALS AND ENGINEERING Unit V.pptx

STRENGTH OF MATERIALS AND ENGINEERING

1. 1 Kongunadu college of engineering and technology (AUTONOMOUS) (Approved by AICTE, New Delhi, Affiliated to Anna University, Chennai, Accredited by NAAC B++ Grade , Accredited by NBA, Recognized by UGC with 2(f) & 12(B) An ISO 9001:2015 certified Institution) Namakkal - Trichy Main Road, Thottiam , Trichy - 621215 Unit V PROPERTIES OF SURFACES by, Dr. P. DINESHKUMAR , M.E., Ph.D., Assistant Professor, Department of Agricultural Engineering, Kongunadu College of Engineering and Technology, Trichy .

2. CENTROID Centroid is defined as the point at which the entire area of the body is assumed to be concentrated. 2

3. CENTRE OF GRAVITY Centre of gravity is defined as an imaginary point at which the entire weight of the body is assumed to act. Let x̄ and ȳ be the co-ordinates of the centre of gravity with respect to some axis of reference, then 3

4. X 1 - The distance of the C.G of the area a 1 from axis OY X 2 - The distance of the C.G of the area a 2 from axis OY X 3 - The distance of the C.G of the area a 3 from axis OY y 1 - The distance of the C.G of the area a 1 from axis OX y 2 - The distance of the C.G of the area a 2 from axis OX y 3 - The distance of the C.G of the area a 3 from axis OX 4

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8. Find the centre of gravity of a 100 mm × 150 mm × 30 mm T-section. 8

9. 9 An I-section has the following dimensions in mm units: Bottom flange = 300 × 100 Top flange = 150 × 50 Web = 300 × 50 Determine mathematically the position of centre of gravity of the section.

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11. A uniform lamina shown in Fig consists of a rectangle, a circle and a triangle. 11

12. A semicircular area is removed from a trapezium as shown (dimensions in mm). Determine the centroid of the remaining area (shown hatched). 12

13. FIRST MOMENT OF AREA First Moment of area is the algebraic sum of the products of the elements of area and the perpendicular distance of the respective element of area from the axis. 13

14. SECOND MOMENT OF AREA Second Moment of area is the algebraic sum of the products of the first moment of area and the perpendicular distance of the respective element of area from the axis. 14

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17. THEOREM OF PERPENDICULAR AXIS It states, If I XX and I YY be the moments of inertia of a plane section about two perpendicular axis meeting at O, the moment of inertia I ZZ about the axis Z-Z, perpendicular to the plane and passing through the intersection of X-X and Y-Y is given by: I ZZ = I XX + I YY 17

18. THEOREM OF PARALLEL AXIS It states, If the moment of inertia of a plane area about an axis through its centre of gravity is denoted by I G , then moment of inertia of the area about any other axis AB, parallel to the first, and at a distance h from the centre of gravity is given by: I AB = I G + ah 2 18

19. Find the moment of inertia about the centroidal X-X and Y-Y axes of the angle section. 19

20. An I-section is made up of three rectangles as shown in figure. Find the moment of inertia of the section about the horizontal axis passing through the centre of gravity of the section. 20

21. Find the moment of inertia of a T-section with flange as 150 mm × 50 mm and web as 150 mm × 50 mm about X-X and Y-Y axes through the centre of gravity of the section. 21

22. Find the moment of inertia of a hollow section about an axis passing through its centre of gravity or parallel X-X axis. 22