Main Menu

See All Software See All Instruments See All Transducers See All Vibration Testing Equipment See All Electroacoustics See All Acoustic End-of-Line Test Systems See All Academy See All Resource Center See All Applications See All Industries See All Services See All Support See All Our Business See All Our History See All Global Presence

Main Menu

See All Analysis & Simulation Software See All DAQ Software See All Drivers & API See All Utility See All Vibration Control See All High Precision and Calibration Systems See All DAQ Systems See All S&V Hand-held Devices See All Industrial Electronics See All Power Analyzer See All S&V Signal Conditioner See All Acoustic Transducers See All Current and Voltage Sensors See All Displacement Sensors See All Force Sensors See All Load Cells See All Multi Component Sensors See All Pressure Sensors See All Strain Sensors See All Strain Gauges See All Temperature Sensors See All Tilt Sensors See All Torque Sensors See All Vibration See All Accessories for Vibration Testing Equipment See All Vibration Controllers See All Measurement Exciters See All Modal Exciters See All Power Amplifiers See All LDS Shaker Systems See All Test Solutions See All Actuators See All Combustion Engines See All Durability See All eDrive See All Production Testing Sensors See All Transmission & Gearboxes See All Turbo Charger See All Training Courses See All Acoustics See All Asset & Process Monitoring See All Custom Sensors See All Durability & Fatigue See All Electric Power Testing See All NVH See All Reliability See All Vibration See All Weighing See All Automotive & Ground Transportation See All Calibration See All Installation, Maintenance & Repair See All Support Brüel & Kjær See All Release Notes See All Compliance

Main Menu

See All nCode - Durability and Fatigue Analysis See All ReliaSoft - Reliability Analysis and Management See All API See All Experimental Testing See All Electroacoustics See All Noise Source Identification See All Environmental Noise See All Sound Power and Sound Pressure See All Noise Certification See All Industrial Process Control See All Structural Health Monitoring See All Electrical Devices Testing See All Electrical Systems Testing See All Grid Testing See All High-Voltage Testing See All Vibration Testing with Electrodynamic Shakers See All Structural Dynamics See All Machine Analysis and Diagnostics See All Dynamic Weighing See All Vehicle Electrification See All Calibration Services for Transducers See All Calibration Services for Handheld Instruments See All Calibration Services for Instruments & DAQ See All On-Site Calibration See All Resources See All Software License Management

Experimental Stress Analysis...

... using Strain Gauges to measure strain on the components' surface. Learn the principle behind the method.

What Is Experimental Stress Analysis?

Experimental Stress Analysis (ESA) is the analysis of the mechanical stress state in materials, which is performed through experiments using strain gauge measurements. Learn the existing types of stress, their origin and states, or how to determine stress from measured strains by reading about it below.

Determining Mechanical Stress 

Stress is defined as the physical response (deformation) in materials caused by force. It usually occurs as a result of an applied force (mechanical stress) that cause the material to deform, but it is also often due to the effects of force within a material or larger system.

Stresses are subdivided as follows:

  • Type: normal stresses and shear stresses
  • Origin: tension, compression, bending, torsion, residual and thermal stresses
  • State: uniaxial, biaxial, triaxial or spatial

Further, stresses pertaining to origin are categorized as normal and shear stresses (when considering the strength of materials, the type of stress is of interest irrespective of its cause). In addition, stresses can be subdivided according to the states described above.

Defining Stress based on its Type and Origin

Unlike other stresses named after their origin, e.g., bending stress, torsion stress, etc., – tensile stress (positive) and compressive stress (negative) occur without any external forces being involved. These comprise normal and shear stresses.

Residual stress (or inherent stress) can occur due to the internal effects of force, e.g.: from non-uniform volume changes in heat-treated parts during the hardening of steel, by non-uniform cooling of cast or injection-molded metal or plastic objects, with welded or forged parts, through mechanical processing, and with larger objects, simply from the effect of their own weight.


Thermal stress is a type of residual stress that occurs in systems, where parts with different thermal expansions are joined together such that free thermal expansion is prevented. It can also occur as a result of non-uniform heating.

Residual and thermal stresses affect the material similar to loading stresses. They reduce the load-bearing capacity of the material owing to externally applied forces. Questions regarding the operational safety of structural parts can therefore only be answered adequately if the residual stresses are known quantitatively and qualitatively. The determination of these stresses is only possible with normal practical methods when they are "released" and the degree of resilient relaxation exhibited by the material in the non-stressed state is measured. The release of these stresses can take place in various ways, such as the hole drilling method or ring core method.

Defining Stress based on its State

Stress states are subdivided as follows:

  1. Uniaxial stress state: It occurs in tension and compression bars only.
  2. Biaxial or planar stress condition: It occurs if the forces producing the stresses occur on two axes that are perpendicular to one another. Resolving the effective directions of the forces into two main axes at 90° is done on theoretical grounds. The effective directions of different forces acting in the same plane, but at different angles, can be very different. However, they can always be resolved into the two main directions.
  3. Triaxial or three-dimensional stress state: This is present if the forces can act in any direction. Similar to the planar stress state, three main axes are defined which are all situated perpendicular to one another.

Strain measurements are restricted because of necessity to the accessible surfaces of the structural parts and can consequently only give information about the stress state at the component's surface. Whereas uniaxial and planar stress states can be analyzed relatively simply using strain measurement techniques, in particular using strain gauges. Three-dimensional stress states present problems since the required measurements along the third axis, i.e., inside the object, are usually not possible to obtain.

However, in a three-dimensional body, which is stressed by external forces, the maximum stress occurs at the surface! (Exception: Hertz effect problems) For the designer, who is usually only interested in the maximum stresses, the determination of the stresses at the surface is sufficient. The internal processes are of lesser significance.

Three-dimensional stress states can only be analyzed using strain measurements if the strain can be measured along the third axis, i.e. in the object's depth. This is found for example in model measuring techniques where strain gauges can be cast into plastic models. This is also possible in civil engineering where strain measuring equipment can be embedded in the concrete during pouring.

Determining Stress from Measured Strains

Mechanical stresses are not accessible for direct measurement. X-ray techniques form an exception to this where the material stresses in the microscopic range can be determined from distortions in the crystal lattice structure, i.e. from the relative changes in the interatomic separation. The process is restricted to layers near the surface of about 5 to 15 μm depth.

Stresses are calculated either according to the theory of materials' strength or using the strain gauge measurements. The latter method is based on Hooke's Law. The mechanical stress is expressed by the quotient of the force F and the cross-sectional area A of the stressed material:

Experimental Stress Analysis

From fatigue testing of an aircraft wing, strain analysis of a printed circuit board, to structural monitoring of a bridge or residual stress measurement, stress analysis strain gauges offer both high performance and cost effectiveness. HBM strain gauges for experimental stress analysis are available in four standard series of high-quality strain gauges and a comprehensive range of strain gauges for special applications such as crack propagation. 

Related Content