2.3.3 - Assumptions Limitations & 2nd Moment of Area | Lecture Note - Edubirdie

University:
McMaster University
Course:
MATLS 2H04 | Introduction to Materials Engineering
Academic year:

2023
Views:

434

Pages:

1
Author:

Sabrina S.

2.3.3 Assumptions, Limitations & 2nd Moment of Area principal axis is one which when bending is applied, will produce pure deformation, which means that the deflection will be perpendicular to the direction of the bending moment any symmetric axis will be a principal axis any axis perpendicular to a principal axis is also a principal axis if a shape has more than 2 symmetric axes (eg square or anus) all axes will be a principal axis Second Moment of Area (around principal axis) (\iint_{A}y^{*}dA) describes how area is distributed w.r.t. the centroid of the cross section commonly used (I_{Z}) rectangle (T_{Z}=\frac{bh^{3}}{12}) Circle (I_{Z}=\frac{\pi\mathcal{R}^{2}}{4}) Parallel Axis Theorem (I_{Z}=I_{Z}+d^{2}A) distance from axis e.g find (I_{Z}) (I_{Z_{1}}=\frac{bh_{1}^{3}}{12}=8\times10^{-8}m^{4}) (I_{Z_{2}}=\frac{b_{2}h_{2}^{3}}{12}=2.88\times10^{-1}m^{4}) Parallel axis theorem (I_{Z_{G}}=I_{Z_{1}}+d^{2}A) (I_{Z_{10}}=285\times10^{-6}\cdot0^{7}1=241\times10^{-6}n^{4})

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