Download presentation

Presentation is loading. Please wait.

Published byJairo Gundy Modified about 1 year ago

1
Geometrical properties of cross-sections Strength of Materials

2
Introduction The strength of a component of a structure is dependent on the geometrical properties of its cross section in addition to its material and other properties. For example, a beam with a large cross section will, in general, be able to resist a bending moment more readily than a beam with a smaller cross-section.

3
Example Shapes

4
Centroid The position of the centroid of a cross- section is the centre of the moment of area of the cross section. If the cross-section is constructed from a homogeneous material, its centroid will lie at the same position as its centre of gravity.

5
First moment of Area Consider an area A located in the x-y plane. Denoting by x and y the coordinates of an element of area d.A, we define the first moment of the area A with respect to the x axis as the integral Similarly, the first moment of the area A with respect to the y axis is defined as the integral

6
First moment of Area It can be conclude that if x and y passes through the centroid of the area of A, then the first moment of the area of S x and S y will be zero.

7
Second moment of Area The second moments of area of the lamina about the x - x and y - y axes, respectively, are given by

8
Second moment of Area From the theorem of Phytagoras : known as the perpendicular axes theorem which states that the sum of the second moments of area of two mutually perpendicular axes of a lamina is equal to the polar second moment of area about a point where these two axes cross.

9
Parallel axes theorem known as the parallel axes theorem, which states that the second moment of area about the X-X axis is equal to the second moment of area about the x-x axis + h 2 x A, where x-x and X-X are parallel.

10
Example 01 Determine the second moment of area of the rectangular section about its centroid (x-x) axis and its base (X-X ) axis. Hence or otherwise, verify the parallel axes theorem.

11
Answer

12
Example 02 Determine the second moment of area about x- x, of the circular cross-section. Using the perpendicular axes theorem, determine the polar second moment of area, namely ‘J’

13
Answer

14

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google