Bending moment in the context of "Cantilever"

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⭐ Core Definition: Bending moment

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported (free to rotate and therefore lacking bending moments) at both ends; the ends can only react to the shear loads. Other beams can have both ends fixed (known as encastre beam); therefore each end support has both bending moments and shear reaction loads. Beams can also have one end fixed and one end simply supported. The simplest type of beam is the cantilever, which is fixed at one end and is free at the other end (neither simple nor fixed). In reality, beam supports are usually neither absolutely fixed nor absolutely rotating freely.

The internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple. For equilibrium, the moment created by external forces/moments must be balanced by the couple induced by the internal loads. The resultant internal couple is called the bending moment while the resultant internal force is called the shear force (if it is along the plane of element) or the normal force (if it is transverse to the plane of the element). Normal force is also termed as axial force.

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👉 Bending moment in the context of Cantilever

A cantilever is a structural element that is firmly attached to a fixed structure at one end and is unsupported at the other end. Sometimes it projects from a vertical surface such as a wall. A cantilever can be in the form of a beam, plate, truss, or slab.

When subjected to a structural load at its far, unsupported end, the cantilever carries the load to the support where it applies a shear stress and a bending moment.

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Bending moment in the context of Beam bridge

Beam bridges are the simplest structural forms for bridge spans supported by an abutment or pier at each end. No moments are transferred throughout the support, hence their structural type is known as simply supported.

The simplest beam bridge could be a log (see log bridge), a wood plank, or a stone slab (see clapper bridge) laid across a stream. Bridges designed for modern infrastructure will usually be constructed of steel or reinforced concrete, or a combination of both. The concrete elements may be reinforced or prestressed. Such modern bridges include girder, plate girder, and box girder bridges, all types of beam bridges.

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Bending moment in the context of Torsion spring

A torsion spring is a spring that works by twisting its end along its axis; that is, a flexible elastic object that stores mechanical energy when it is twisted. When it is twisted, it exerts a torque in the opposite direction, proportional to the amount (angle) it is twisted. There are various types:

  • A torsion bar is a straight bar of metal or rubber that is subjected to twisting (shear stress) about its axis by torque applied at its ends.
  • A more delicate form used in sensitive instruments, called a torsion fiber consists of a fiber of silk, glass, or quartz under tension, that is twisted about its axis.
  • A helical torsion spring, is a metal rod or wire in the shape of a helix (coil) that is subjected to twisting about the axis of the coil by sideways forces (bending moments) applied to its ends, twisting the coil tighter.
  • Clocks use a spiral wound torsion spring (a form of helical torsion spring where the coils are around each other instead of piled up) sometimes called a "clock spring" or colloquially called a mainspring. Those types of torsion springs are also used for attic stairs, clutches, typewriters and other devices that need near constant torque for large angles or even multiple revolutions.
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Bending moment in the context of I-beam

An I-beam is any of various structural members with an Ɪ- (serif capital letter 'I') or H-shaped cross-section. Technical terms for similar items include H-beam, I-profile, universal column (UC), w-beam (for "wide flange"), universal beam (UB), rolled steel joist (RSJ), or double-T (especially in Polish, Bulgarian, Spanish, Italian, and German). I-beams are typically made of structural steel and serve a wide variety of construction uses.

The horizontal elements of the Ɪ are called flanges, and the vertical element is known as the "web". The web resists shear forces, while the flanges resist most of the bending moment experienced by the beam. The Euler–Bernoulli beam equation shows that the Ɪ-shaped section is a very efficient form for carrying both bending and shear loads in the plane of the web. On the other hand, the cross-section has a reduced capacity in the transverse direction, and is also inefficient in carrying torsion, for which hollow structural sections are often preferred.

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