Axial Load and Axial Force in Structural Analysis

What Is Axial Load?

An axial load is an external force applied along the longitudinal axis of a structural member. When the load acts through the centroid of the cross-section, it produces primarily axial tension or compression. If the load is applied eccentrically, the member is subjected to combined axial force and bending. 

The force acts parallel to the member axis. In an ideal case, the load passes through the centroid of the cross-section, producing a uniform axial response. 

Depending on its direction, an axial load can create: 

• Tension, which pulls and elongates the member 
• Compression, which pushes and shortens the member 

For example, a hanging rod supporting a suspended load is subjected to tensile axial loading, while a building column carrying gravity loads experiences mostly compressive axial loading. 

Axial loads are common in many structural applications, including columns, braces, truss members, tie rods, cables, bolts, and lifting structures.

What Is Axial Force?

Axial force is the internal force developed because of applied loads, support reactions, imposed displacements, temperature effects, restressing, constraints, and load transfer through connected members. Unlike an applied load, which acts on the structure from outside, axial force is the resultant internal normal force acting across a member cross-section and required to satisfy equilibrium. It acts along the longitudinal axis of the element and tends to either stretch the member (tension) or shorten it (compression). 

In mechanics, these internal actions include normal (axial) forces, shear forces, bending moments, and torsional moments. Axial force, also referred to as a normal force, acts along the member to the examined cross-section and is responsible for tensile or compressive behavior. 

Axial force is the internal force that develops within a structural member to resist an externally applied load. It acts along the member’s longitudinal axis and can occur in two forms: 

• Tensile axial force (positive): the member is being stretched. 
• Compressive axial force (negative): the member is being shortened. 

The magnitude and sign of the axial force depend on the equilibrium of the member and the loads acting on it. Unlike axial load, which is an external action applied to a structure, axial force represents the internal force that exists within the member itself. 

Image: Axial force illustration

In structural analysis and FEA software, axial force is commonly denoted by N. It is typically presented as an internal result for beam, frame, or truss elements and may be shown in force tables or axial force diagrams. Depending on the adopted sign convention, positive values often indicate tension and negative values indicate compression. 

Axial Load vs Axial Force: Key Difference

An axial load is an external action applied to a structure, while axial force is the internal response developed within a member to resist that loading. The final axial force value depends not only on the applied load itself but also on support conditions, constraints, and the behavior of the entire structural system. 

Tension and Compression Under Axial Loading

When a structural member is subjected to axial loading, the internal response appears as axial (normal) force, which can act in either tension or compression depending on the direction of loading and boundary conditions. 

A tensile axial force occurs when the internal force tends to elongate the member. The material fibers are pulled apart, and the member is subjected to stretching along its longitudinal axis. 

A compressive axial force occurs when the internal force tends to shorten the member. The material fibers are pushed together, and the member resists shortening along its axis. 

The sign assigned to tensile and compressive forces depends on the adopted convention. Under the sign convention used in this example, tension is positive and compression is negative. Analysis software may use a different convention, particularly for element-end forces and internal force outputs, so engineers should always verify the solver documentation and element local axis orientation before interpreting results. 

Both tensile and compression forces are structurally important, but they can lead to different failure mechanisms. Members subjected to tension typically fail when the material reaches its strength limit. For example, bolts and tie rods may fail under excessive tensile loading because they cannot buckle. Compression members, on the other hand, may fail either by material crushing or by buckling instability. Slender columns and braces are particularly sensitive, as small imperfections or load eccentricities can cause the member to lose stability and buckle before reaching its ultimate material strength. 

Average Axial Stress and Its Relationship to Axial Force

The relationship between axial stress and axial force is commonly used to estimate the behavior of members subjected to pure axial loading. For a simple prismatic member with a uniform cross-section, axial stress can be calculated as: 

σ = F / A 

where: 

• σ = axial stress 
• F = axial force 
• A = cross-sectional area 

The equation can also be rearranged to determine axial force: 

\( N = \sigma_{\text{avg}} A \)

These equations assume that stress is evenly distributed across the cross-section and that the member is subjected to concentric axial loading. They provide the average normal stress in a simple member and are widely used in mechanics of materials. However, they do not determine axial force distribution in general frames, trusses, or FEA models, where internal forces are obtained through equilibrium equations and structural analysis. 

Examples of Axial Load and Axial Force in Structures

Some common examples include: 

• Column under vertical load – Columns primarily carry compressive axial forces generated by gravity loads transferred from beams, floors, or other structural components. 
• Brace in a frame – Structural braces resist lateral actions such as wind or seismic loading and can experience either tensile or compressive axial force depending on the loading direction. 
• Truss member – Ideally, truss members carry only axial tension or compression. In practice, secondary bending may also occur because of connection details, member self-weight, eccentricities, or loads applied between joints. 
• Beam-column with axial force and bending – In practical structures, members often carry combined loading. A beam-column may experience axial force together with bending moments, creating a more complex stress distribution. 
• Lifting, offshore, and heavy equipment structures – Cranes, lifting frames, offshore modules, and similar systems frequently contain members subjected to significant axial loading. In these applications, axial force is usually evaluated together with dynamic effects, stability requirements, and code-based design checks. 

How to Read an Axial Force Diagram

An axial force diagram shows how internal axial force changes along the length of a structural member such as a beam, column, cable, or truss element. 

What the diagram shows 

The horizontal axis represents the position along the member, and the vertical axis represents the corresponding internal axial force. The diagram illustrates how axial force changes from one cross-section to another.  

Positive and negative axial force 

The sign of the force indicates the loading type: 

• Positive values → tensile axial force 
• Negative values → compressive axial force 

The exact convention can vary depending on the software or design standard used. 

Constant axial force zones 

For a straight one-dimensional member, the axial force remains constant between two points if there is no distributed axial load or other axial force transfer along that segment. These regions appear as horizontal segments in the diagram. 

Jumps at applied loads and supports 

Sudden changes in the diagram occur at locations where concentrated loads or support reactions introduce an axial force component.  The magnitude of the jump is equal to the component of the applied force acting along the member’s local axis. 

Simple example 

Consider a straight bar fixed at one end and subjected to two axial point loads of 20 kN and 10 kN acting along its axis. From equilibrium, the support reaction is 30 kN. 

To calculate the axial force, make section cuts between the loads and apply equilibrium equations to each segment: 

• Segment 1 (support to first load): N = 30 kN 
• Segment 2 (between the loads): N = 10 kN 
• Segment 3 (beyond the second load): N = 0 kN 

This piecewise result can then be used to draw the axial force diagram. The diagram consists of three constant-force regions separated by abrupt jumps at the load application points. Each jump is equal to the magnitude of the corresponding axial point load. 

If the first segment has a cross-sectional area of 1,000 mm², the average axial stress is: 

σ = N/A = 30,000 N / 1,000 mm² = 30 MPa 

Image: Axial force diagram example with support reactions and stress calculation 

This axial force diagram example demonstrates how support reactions, section cuts, equilibrium equations, and the axial stress formula are used together to determine internal forces in a member under axial loading. 

Axial Load and Axial Force in FEA

In Finite Element Analysis (FEA), axial force is a standard result output for beam, truss, and frame elements. However, interpreting axial-force results requires more than simply reading a single value from the postprocessor. 

When reviewing axial force in FEA, engineers should consider: 

• Load cases, load combinations, and envelopes, which may produce different governing axial forces 
• Element type and formulation (beam, truss, nonlinear elements, etc.) 
• Local coordinate system orientation, since axial force is defined along the element’s local axis 
• Sign convention and element-end force definitions, which can vary between solvers 
• Result location or station along the element where the force is reported 
• Linear versus nonlinear analysis assumptions 
• Tension-only or compression-only element behavior, where applicable  

Axial force should also be evaluated together with bending moments, shear forces, buckling effects, and code-based resistance checks. On its own, axial force rarely provides sufficient information for structural verification, particularly in members where combined loading governs the design. 

The final axial force value depends not only on the individual loads included in a load combination but also on the load factors applied to each load case. As a result, different combinations and envelopes may produce significantly different governing axial forces in the same member. 

A critical aspect in FEA interpretation is the element coordinate systems in FEA. For one-dimensional beam, frame, bar, and truss elements, axial force is typically reported along the element’s longitudinal local axis, which may be designated as local x, local 1, or another solver-specific axis. Misinterpreting the local axis orientation or sign convention can lead to incorrect conclusions about whether a member is in tension or compression. 

For shell and solid elements, a single member-level axial force result is usually not available. Instead, engineers typically evaluate stresses, membrane-force resultants, section forces, or forces integrated across a section cut to assess axial loading effects. 

Axial force must also be evaluated together with: 

• bending moments 
• shear forces 
• stability effects such as buckling 
• code-based resistance checks 

On its own, axial force does not provide sufficient information for structural verification, especially in members where combined loading governs design. 

This is why many engineering teams use structural analysis and design software SDC Verifier. The software helps engineers use FEA results in a structured verification workflow. It can recognize structural details, organize load cases and combinations, perform code-based strength and stability checks, and generate reports that update with the calculation model. 

Axial Load vs Radial Load

The difference between axial and radial loads lies in the direction of force application relative to the member or component axis. 

Image: Axial and radial loads acting on a bearing 

Common Mistakes When Interpreting Axial Force

Focusing on a single axial force value without considering the broader structural context can lead to incorrect engineering conclusions. 

Some common mistakes include: 

• Confusing applied load with internal force – An axial load is an external action, while axial force is the internal response developed within the member. 
• Ignoring sign convention – Tension and compression are identified through sign conventions, which may differ between analysis software and design standards. 
• Checking axial stress without considering buckling checks – A compression member may fail due to instability long before its material strength limit is reached. 
• Ignoring combined axial force and bending – Many structural members behave as beam-columns, where the interaction between axial force and bending moments governs the design. 
• Reading the global direction instead of the local member axis – In FEA models, axial force is typically reported in the element’s local coordinate system. Misinterpreting local and global directions can lead to incorrect assessment of tension and compression. 
• Evaluating a single load case instead of load combinations or envelopes – The critical axial force often occurs under a specific load combination rather than an individual load case. 
• Treating all element types alike – An axial force result reported for beam or truss elements is not directly equivalent to stress output from shell or solid elements. The appropriate result quantity depends on the element formulation and the selected verification approach.

FAQ

What is axial load? 

An axial load is a force applied parallel to the longitudinal axis of a member. Depending on its direction, it places the member in either tension or compression. 

What is axial force? 

Axial force is the internal force that acts along a member’s axis in response to external loading. It represents the tension or compression developed within the member. 

Are axial load and axial force the same? 

An axial load refers to an external action applied along a member axis, while axial force refers to the internal section force that develops within the member. The terms are sometimes used interchangeably in less formal contexts, but they describe different roles in structural analysis. 

How is axial force calculated? 

There is no single universal formula for axial force in a complete structure. Axial force is typically determined from equilibrium equations or structural analysis. For a simple member with known average normal stress, the relationship is: 

\( F = \sigma_{\text{avg}} A \)

where F is axial force, σ is axial stress, and A is the cross-sectional area. 

What does an axial force diagram show? 

An axial force diagram shows how the internal axial force changes along the position of a member. It helps identify regions subjected to tension or compression and locate critical force values. 

Is tension positive or negative? 

The sign convention depends on the adopted standard or software. In many engineering applications, tension is considered positive and compression negative, but the opposite convention may also be used. 

What is the difference between axial and radial load? 

An axial load acts parallel to the axis of a member or component and produces tension or compression. A radial load acts perpendicular to the axis and typically introduces transverse forces and bending effects.