什么是弯矩、力矩和阻力矩

忒修斯破船2024-03-25 08:54:42  113

这是一篇介绍结构力学知识的小文章。

To understand the term Moment of Resistance first we have to understand what is bending moment and to understand that we have to understand what is the moment of force.

要理解阻力矩这个术语,首先我们必须了解什么是弯矩,并且要理解什么是力矩。

Force 力

The basic definition of force that we have learned is that force is pushing and pull. Force, when applied to an object, tends to change its motion or its shape.

我们所学到的力的基本定义是:力是推力和拉力。力作用在物体上,往往会改变物体的运动或形状。

In structural engineering, we have well-defined cross-sections and the members have a longitudinal axis and a lateral axis

在结构工程中,我们有明确定义的横截面,杆件有纵轴和横轴

A force applied in the longitudinal axis of the member would tend to elongate (Tensile Force) or compress (Compressive Force) the member.

施加在杆件纵轴上的力会倾向于使杆件伸长(拉力)或压缩(压力)。

A force applied in the lateral axis would try to slice off the member (Shear force) or would try to bend the member (Bending Moment).

施加在侧轴上的力将尝试切掉杆件(剪切力)或尝试弯曲杆件(弯矩)。

How and why is bending moment different from the other three?弯矩与其他三种弯矩有何不同以及为什么不同?

The amount of elongation, compression or shearing is directly dependent on the magnitude of the force applied. More is the force more is it effective.But the same is not the case with rotation. The same amount of force if applied at a greater distance would produce greater rotation.

拉伸、压缩或剪切的程度直接取决于所受力的大小。力越大,效果越好。但旋转的情况并非如此。同样的力如果施加在更大的距离上,就会产生更大的旋转。

In the above figure with the same magnitude of force(F) the rotation would be more in the second case since the lever arm is more and thus the moment is more. Thus it’s not the magnitude of the force but also the distance at which it is applied that tells us about its effect. So we multiplied the two quantities and gave it a name as the moment of force.

在上图中,在力(F)大小相同的情况下,第二种情况下的旋转会更大,因为杠杆臂更大,因此力矩更大。因此,不是力的大小,而是施加力的距离能告诉我们力的作用效果。因此,我们将这两个量相乘,并给它起了一个名字作为力矩。

The turning effect of a force is known as the moment. Moment of force is the product of force and the distance of the force from the point of interest. If this moment of force tries to twist the member then we call it a twisting moment or torsional moment and if this moment of force tries to bend the member then we call it bending moment.

力的转动效应称为弯矩。力矩是力和力与目标点的距离的乘积。如果这个力矩试图扭转杆件,那么我们称之为扭转力矩或扭转力矩,如果这个力矩试图弯曲杆件,那么我们称之为弯矩。

Moment of Resistance 阻力矩

When a body is strained it tries to resist that by generating internal stresses. Stress is the resistance offered by a body to an external force.

当物体受到应力时,它试图通过产生内力来抵抗它。应力是物体对外力提供的阻力。

When a beam bends the concave face of the beam is under compression and the convex face is under tension. These compressive and tensile strains produce compressive and tensile stresses (resistance) in the beam respectively. The couple formed by these resistive forces is termed as a moment of resistance.

当梁弯曲时,梁的凹面处于压缩状态,凸面处于张力状态。这些压缩应变和拉伸应变分别在梁中产生压缩应力和拉伸应力(阻力)。由这些阻力形成的耦合被称为抵抗时刻。

Ultimate Moment of Resistance 极限抵抗力矩

If we consider the compressive and tensile stress in the beam to be equal to the tensile and compressive strength of the material then the couple formed by them is termed as ultimate moment of resistance or the Ultimate Bending Moment since the beam cannot take bending moment more than that.

如果我们认为梁中的压应力和拉应力等于材料的抗拉强度和抗压强度,那么它们形成的耦合称为极限抗力矩或极限弯曲力矩,因为梁承受的弯曲力矩不能超过这个值。

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