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# Algorithms for Determining Physical Responses of Structures Under Load

- Created: Saturday, 01 September 2012

### Structure can be monitored in real time while in actual service.

Ultra-efficient real-time structural monitoring algorithms have been developed to provide extensive information about the physical response of structures under load. These algorithms are driven by actual strain data to measure accurately local strains at multiple locations on the surface of a structure. Through a single point load calibration test, these structural strains are then used to calculate key physical properties of the structure at each measurement location. Such properties include the structure’s flexural rigidity (the product of the structure’s modulus of elasticity, and its moment of inertia) and the section modulus (the moment of inertia divided by the structure’s half-depth). The resulting structural properties at each location can be used to determine the structure’s bending moment, shear, and structural loads in real time while the structure is in service.

Cantilever Beam of tapered cross section subjected to tip loading." class="caption" align="right">The amount of structural information can be maximized through the use of highly multiplexed fiber Bragg grating technology using optical time domain reflectometry and optical frequency domain reflectometry, which can provide a local strain measurement every 10 mm on a single hair-sized optical fiber. Since local strain is used as input to the algorithms, this system serves multiple purposes of measuring strains and displacements, as well as determining structural bending moment, shear, and loads for assessing real-time structural health.

The first step is to install a series of strain sensors on the structure’s surface in such a way as to measure bending strains at desired locations. The next step is to perform a simple ground test calibration. For a beam of length l (see example), discretized into n sections and subjected to a tip load of P that places the beam in bending, the flexural rigidity of the beam can be experimentally determined at each measurement location x. The bending moment at each station can then be determined for any general set of loads applied during operation.

*This work was done by W. Lance Richards
and William L. Ko of Dryden Flight Research
Center. DRC-008-023*