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Strength of materials - Chapter 6: Properties of cross sectionss - Nguyễn Sỹ Lâm

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.
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  1. 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)
  2. 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
  3. 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:
  4. 6.1 CENTER OF GRAVITY - CENTROID
  5. 6.1 CENTER OF GRAVITY - CENTROID
  6. 6.1 CENTER OF GRAVITY - CENTROID
  7. 6.1 CENTER OF GRAVITY - CENTROID
  8. 6.2 MOMENT OF INERTIA OF AN AREA (1) MOMENT OF INERTIA WITH RESPECT TO AN AXIS Moment of inertia of an irregular are
  9. 6.2 MOMENT OF INERTIA OF AN AREA
  10. 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)
  11. 6.3 MOMENT OF INERTIA OF COMPOSITE AREAS
  12. 6.3 MOMENT OF INERTIA OF COMPOSITE AREAS (1) Parallel axis theorem
  13. 6.3 MOMENT OF INERTIA OF COMPOSITE AREAS (1) Parallel axis theorem - Example
  14. 6.3 MOMENT OF INERTIA OF COMPOSITE AREAS (2) Rotation of axes – Transformation of inertia moment of an area
  15. 6.4 RADIUS OF GYRATION