Name: eccentric load stresses in structural columns
Uploaded: 2024-05-23T13:00:08.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Physics

PHYS.2

PHYS.2.D

design-of-columns-under-an-eccentric-load

Design of Columns under an Eccentric Load

対称面に偏心軸荷重がかかる柱の場合、偏心荷重による垂直応力は、等価な中心荷重と曲げによる応力として記述できます。
偏心荷重のある柱を設計する際、柱に発生する最大応力は最大許容応力を超えてはなりません。この条件は、2 つの異なるアプローチを使用して満たすことができます。
許容応力法では、偏心荷重を受けた柱の許容応力が、中央荷重を受けた柱の最大応力と同じであると仮定します。カラムの許容応力は、細長率の関数として表すことができます。
中心荷重の許容応力は、曲げモーメントによる応力よりも小さくなります。これにより、許容応力法は過度に保守的になります。 
一方、相互作用法では、中心荷重と曲げによる許容応力が考慮されます。
これは、カップルモーメントがない場合の中心荷重下での最大応力の方程式を提供します。同様に、荷重がない場合の純粋な曲げによる最大応力を定義します。

偏心荷重下の柱の設計

偏心荷重に耐えられるように柱を設計することは、構造が故障することなく偏心荷重を確実に支えられるようにするための構造工学の重要な側面です。この設計プロセスでは、柱の応力分布と全体の安定性に大きな影響を与える可能性がある、偏心荷重によって導入される追加の垂直応力を考慮する必要があります。柱に偏心荷重が加わると、垂直応力が誘発されます。垂直応力は、等価の中心荷重と追加の曲げ応力による応力の組み合わせとして概念化できます。これにより応力が不均一に分布することになり、構造的な破損を防ぐために慎重に分析する必要があります。偏心荷重がかかる柱の設計では、許容応力法と相互作用法という 2 つの主な方法が使用されます。

許容応力法は、偏心して荷重がかかる柱の許容応力を、中心に荷重がかかる柱に許容される最大応力と等しくする単純なアプローチです。この方法は、柱の細長比（荷重下での座屈傾向を測る指標）を関数として扱い、設計プロセスを単純化します。ただし、この方法では、中心荷重の許容応力には曲げによる追加応力が含まれることが前提となっているため、材料の可能性を最大限に活用できない保守的な設計になる可能性があります。このアプローチに固有の保守主義により安全性は確保されますが、必要以上に大型で高価な柱が必要になる可能性があります。

相互作用法は、中心荷重による許容応力と曲げモーメントから生じる応力の両方を考慮することにより、より微妙なアプローチを提供します。 この方法は、偶モーメントなしで柱が耐えることができる最大応力 (純粋な中心荷重) と純粋な曲げによる最大応力 (軸方向荷重なし) を計算するためのフレームワークを提供します。これらの条件を同時に考慮することにより、相互作用法により、偏心荷重がかかった柱の許容応力をより正確に、あまり保守的に見積もることができます。

実際には、安全性と材料効率のバランスをとる能力により、相互作用法が好まれることがよくあります。軸方向荷重と曲げモーメントの両方を考慮して、柱内の応力分布を詳細に分析する必要があります。

対称面に偏心軸荷重がかかる柱の場合、偏心荷重による垂直応力は、...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Columns

カラム

KEY TERMS AND CONCEPTS

主要用語と概念

eccentric load stresses in structural columns

Structural columns under eccentric load must be designed for both axial force and bending stress. An eccentric load is an off-center load, and it creates a non-uniform stress pattern across the column. Engineers must analyze this stress distribution carefully to reduce the risk of failure.

The stress in an eccentrically loaded column can be treated as the sum of two parts. One part comes from an equivalent centric load, which is a load applied through the center of the column. The other part comes from bending stresses caused by the load being off-center.

Two common design approaches are used for these columns. The allowable stress method sets the allowable stress for an eccentrically loaded column equal to the maximum stress allowed for a centrally loaded column. This method uses the column slenderness ratio, which describes how likely a column is to buckle.

The allowable stress method is simple, but it is also conservative. It assumes the centric-load allowable stress already covers the extra bending stress from eccentric loading. As a result, the column may be larger and more expensive than needed, even though the design is safe.

The interaction method gives a more detailed design check. It considers both the allowable stress from centric loading and the stress from bending moment at the same time. It compares the case of pure centric loading, with no couple moment, and the case of pure bending, with no axial load.

Because it includes both effects, the interaction method can estimate allowable stress more accurately. It is often preferred when engineers want a better balance between safety and material use. The method requires careful stress analysis of the column under both axial load and bending moment.

Eccentric Load Stresses in Structural Columns

eccentric-load-stresses-in-structural-columns

stability of structures

Critical Load and Structure Stability

Structural stability is an important idea in mechanical engineering. It helps engineers design buildings, vehicles, and machines that stay safe and efficient under load. A simple model for studying this behavior uses two rods joined at a pivot point O with a torsional spring, which is a spring that resists twisting, at the pivot. The setup is similar to a scissor jack used to lift a car. In the example, the linkage arms are vertical, which matches the case where the vehicle has been raised as...

euler&#39;s formula for pin-ended columns

Critical Buckling Load in Pin-Ended Columns

Critical buckling load in pin-ended columns is a key idea in structural engineering. It explains when a column under compressive axial load becomes unstable and starts to buckle. A pin-connected column with a centric load F at one end has a reaction force of F' = -F at the other end. When the applied load rises above the critical load, buckling begins. To find the critical load, the column PQ can be treated like a vertical beam. Point O is chosen on the elastic curve of the beam at a distance...

euler&#39;s formula to columns with other end conditions

euler-s-formula-to-columns-with-other-end-conditions

Euler Buckling for Different Column Supports

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euler&#39;s formula to columns: problem solving

euler-s-formula-to-columns-problem-solving

Spring-Loaded Column Buckling Analysis

Spring-loaded column buckling analysis uses static equilibrium to find the critical load in a rigid bar system. The setup has two equal-length rigid bars, AB and BC, joined at pivot point B. A tension spring with constant k is attached to B and pulls horizontally. A vertical load F is applied at point A, and the bars rotate around the pivot like a knee joint. As point B moves, the spring stretches by an amount X. The spring then pushes back against the sideways motion of B. To study the...

eccentric loading

Column Bending Under Off-Center Load

Eccentric loading shows how a column bends when a force is applied off-center. In structural engineering, this matters because the load no longer acts along the centroidal axis, so the column sees both direct compression and bending stress. The off-center force can be treated as two parts. One part is a centric load F that acts along the column’s axis. The other part is a couple moment created by the eccentricity, or distance, between the load and the centroidal axis. To study the column...

design of columns under a centric load

Column Buckling and Load Design Basics

Column design under a centric load is a key part of structural engineering. It helps engineers keep buildings and other structures stable and safe. The main tools used here are Euler’s formula and Secant’s formula. Euler’s formula is used when a column is assumed to be perfect, straight, and uniform. It also applies when the material stays within its elastic limit. The critical load from Euler’s formula depends on the material’s modulus of elasticity and the column’s shape. This formula works...

design of columns under an eccentric load

Structural columns under eccentric load must be designed for both axial force and bending stress. An eccentric load is an off-center load, and it creates a non-uniform stress pattern across the column. Engineers must analyze this stress distribution carefully to reduce the risk of failure. The stress in an eccentrically loaded column can be treated as the sum of two parts. One part comes from an equivalent centric load, which is a load applied through the center of the column. The other part...

key terms and concepts

Learn how eccentric loads create combined axial and bending stresses in columns, and compare the allowable stress and interaction methods used in design.

Eccentric Load Stresses in Structural Columns | JoVE K12

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Eccentric Load Stresses in Structural Columns

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