›
›

Bài giảng Strength of materials - Chương 6: Properties of cross sections - Nguyễn Sỹ Lâm

Download
CHAPTER 6: PROPERTIES OF CROSS SECTIONS  
6.0 Introduction  
6.1 Center of Gravity – Centroid  
(trọng tâm – “trọng tâm” hình học)  
6.2 Moment of Inertia of an area  
(Moment quán tính của một “mặt cắt ngang”)  
6.3 Moment of Inertia of composite area  
(Moment quán tính của một “mặt cắt ngang” phức tạp)  
6.4 Radius of Gyration  
(bán kính quán tính – bán kính của sự vặn xoắn)  
6.0 INTRODUCTION  
Not only area but also other geometrical  
characteristics affecting to the resistance  
of the beam  
Called:  
CROSS-SECTIONAL PROPERTIES  
Relative resistance of 4 beam cross-sections (with the  
same cross-section areas) to bending stress and  
deflection  
6.1 CENTER OF GRAVITY - CENTROID  
Center of gravity or center of mass, refers to weights or masses and  
can be thought of a single point at which the weight could be held and  
be in balance in all directions.  
Centroid usually refers to the center of lines, areas and volumes.  
The centroid of cross-sectional areas (of beams and columns) will be  
used later as the reference origin for computing other section  
properties.  
If the weight or object were homogeneous, the center of gravity and the  
centroid would coincide.  
CENTER OF GRAVITY  
CENTROID  
6.1 CENTER OF GRAVITY - CENTROID  
First moment of an area about an axis (Moment tĩnh của một tiết  
diện quanh môt trục)  
6.1 CENTER OF GRAVITY - CENTROID  
PROPERTIES:  
(1) Consider a moment of an area A with respect to an u-axis: Su  
If Su = 0 then u is called central axis (trục trung tâm) and the centroid  
lies on u-axis  
(2) If u-axis and v-axis are central axes which mean: Su = 0 and Sv = 0  
then the intersection of the two axes is the centroid.  
(3) Coordinates of the centroid C(xC, yC)can be calculated as follows:  
6.1 CENTER OF GRAVITY - CENTROID  
DEMONSTRATION:  
6.1 CENTER OF GRAVITY - CENTROID  
6.1 CENTER OF GRAVITY - CENTROID  
6.1 CENTER OF GRAVITY - CENTROID  
6.1 CENTER OF GRAVITY - CENTROID  
6.1 CENTER OF GRAVITY - CENTROID  
6.1 CENTER OF GRAVITY - CENTROID  
EXAMPLE  
6.1 CENTER OF GRAVITY - CENTROID  
6.1 CENTER OF GRAVITY - CENTROID  
6.2 MOMENT OF INERTIA OF AN AREA  
(1) MOMENT OF INERTIA WITH RESPECT TO AN AXIS  
Moment of inertia of an irregular are  
6.2 MOMENT OF INERTIA OF AN AREA  
6.2 MOMENT OF INERTIA OF AN AREA  
6.2 MOMENT OF INERTIA OF AN AREA  
6.2 MOMENT OF INERTIA OF AN AREA  
(2) POLAR MOMENT OF INERTIA (moment quán tính độc cực)  
r
(3) PRODUCT OF INERTIA OF AN AREA (moment quán tính ly tâm)  
6.2 MOMENT OF INERTIA OF AN AREA  
NOTES  
If Ixy = 0 then (x, y) are principle axes of inertia  
If (x, y) are the central axes, which mean Sx = 0 and Sy = 0, and Ixy = 0  
then (x, y) are central principle axes of inertia  
Tải về để xem bản đầy đủ
pdf 30 trang Thùy Anh 15940 Free
Download
Bạn đang xem 20 trang mẫu của tài liệu "Bài giảng Strength of materials - Chương 6: Properties of cross sections - Nguyễn Sỹ Lâm", để tải tài liệu gốc về máy hãy click vào nút Download ở trên

File đính kèm:

  • pdfbai_giang_strength_of_materials_chuong_6_properties_of_cross.pdf