Composite areas are structures with multiple basic shapes connected in some way. These shapes usually include rectangles, triangles, circles, and other basic shapes that are connected in such a way as to form a single structure. Calculating the second moment of area for a composite area is essential when trying to understand the structure's overall stiffness.

The second moment of area, also known as the moment of inertia, measures a structure's resistance to bending. It is calculated by determining the distribution of the structure's area around an axis called the reference axis. For a composite area, finding the second moment of area involves splitting the composite shape into its fundamental components, finding their respective centroids, calculating the second moments of area along the reference axes for each component using the parallel axes theorem, and summing these moments to obtain the total.

To calculate the second moment of area for a composite area, such as an L beam, several steps must be taken. The first step involves identifying the centroids of the individual, perpendicular rectangular sections, followed by using these centroids to calculate the centroid for the entire beam. Next, the second moment of area for each rectangular section is determined by multiplying the width by the height cubed and dividing the result by twelve.

To obtain the total second moment of area for the beam, the distance from each rectangular section's centroid to the beam's centroid is substituted into the parallel axis theorem formula. This formula facilitates the calculation of each rectangular section's second moment of area along the reference axis by utilizing the distance between the section's centroid and the beam's centroid. Once the second moment of area for each rectangular section has been determined, it is necessary to add them together to obtain the beam's total second moment of area. This value is critical in assessing the beam's ability to withstand bending stress and must be accurately estimated for safe and effective design.

Tags
Moments Of InertiaComposite AreasSecond Moment Of AreaStiffnessBending ResistanceReference AxisCentroidsParallel Axes TheoremL BeamRectangular SectionsCalculation StepsBeam Design

来自章节 10:

article

Now Playing

10.6 : Moments of Inertia for Composite Areas

Moment of Inertia

897 Views

article

10.1 : 区域的惯性矩

Moment of Inertia

796 Views

article

10.2 : 面积的平行轴定理

Moment of Inertia

1.1K Views

article

10.3 : 区域的回转半径

Moment of Inertia

1.1K Views

article

10.4 : 面积主弯矩

Moment of Inertia

861 Views

article

10.5 : 惯性矩:解决问题

Moment of Inertia

494 Views

article

10.7 : 面积的惯性积

Moment of Inertia

383 Views

article

10.8 : 关于斜轴的区域的惯性矩

Moment of Inertia

539 Views

article

10.9 : 惯性矩的莫尔圆

Moment of Inertia

391 Views

article

10.10 : 惯性矩莫尔圆:问题解决

Moment of Inertia

1.6K Views

article

10.11 : 质量惯性矩

Moment of Inertia

585 Views

article

10.12 : 质量惯性矩:问题解决

Moment of Inertia

241 Views

JoVE Logo

政策

使用条款

隐私

科研

教育

关于 JoVE

版权所属 © 2025 MyJoVE 公司版权所有,本公司不涉及任何医疗业务和医疗服务。