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A strain-based load identification model for beam structures subjected to multiple loads is presented. The number of sensors for the load identification model is the same as the number of load conditions acting on a beam structure. In the model, the contribution of each load to the strains measured by strain sensors is defined. In this paper, the longitudinal strains measured from multiplexed fiber Bragg grating (FBG) strain sensors are used in the load identification. To avoid the dependency on the selection of locations for FBG sensors installed on a beam structure, the measured strain is expressed by a general form of a strain sensing model defined by superimposing the distribution shapes for strains from multiple loads. Numerical simulation is conducted to verify the model. Then, the load identification model is applied to monitoring of applied loads on a 4 m-long steel beam subjected to two concentrated loads. In the experiment, seven FBG sensors and nine electrical strain gages (ESGs) were installed on the surface of the bottom flange. The experimental results indicate a good agreement between estimated loadings from the model and the loads applied by a hydraulic jack.

To secure the safety of a beam structure subjected to multiple loads such as gravity-induced loads, earthquakes, winds, or unexpected loads, the maximum stress in a beam structure is measured and checked not to ensure it does not exceed the allowable stress of a member [

Using the measured strains from strain sensors, the safety of a beam structure can be managed by controlling the level of maximum strain. To control the level of strain in a beam structure, it is necessary to identify the magnitude of all the loads acting on the beam structure. Various techniques to estimate the magnitudes of loads acting on structures have been reported [

Long gauge fiber optic sensors (LGFOSs), vibrating wire strain sensors (VWSGs), and fiber Bragg grating (FBG) strain sensors have been utilized in the estimation of maximum strains of beam structures [

Therefore, in this paper, a strain-based load identification model for beam structures subjected to multiple loads is presented. Using the strains measured by multiplexed FBG strain sensors, the contribution of each load on the measured strains is defined to identify the loads acting on a beams structure. The number of sensors for the load identification model is set to the same as the number of load conditions acting on the beam structure. Firstly, a numerical simulation is conducted to verify the model. Then, the load identification model is applied to monitoring of applied loads on a 4 m-long steel beam subjected to two concentrated loads. In the experiment, for comparison of the estimated loads based on the model and the applied loads from a hydraulic jack, seven FBG sensors and nine electrical strain gages (ESGs) were installed on the surface of the flange.

The strain sensing model is presented to define the total strain measured at a specific point in a beam structure. The total strain can be found by superimposing the strains due to loadings acting separately. Instead of measuring the strain at a specific point where sensor is installed, to derive general form of strain sensing model, the deformed shape caused by the multiple loadings is needed to be defined by superimposing the distribution shape of strains along the length of a beam for each loading separately. Using the deformed shape of a beam structure subjected to multi-loadings, the total strain at an arbitrary point in a beam structure can be defined.

Based on general concepts in engineering mechanics, as shown in _{FBG}_{FBG}

Then, the general form for the longitudinal strain _{FBG}

On the basis of principle of superposition, as shown in _{t}_{j}_{t}_{k}_{j}

Using measured strains from _{i}_{FBG}^{k}^{k}^{k}

Then, the total strain _{t}

In this paper, the loads acting on a beam structure are identified by the strains measured by FBG strain sensors. As given in _{j}_{j}_{j}_{j}_{j}_{j}_{j}_{j}

The beam member in a building frame in _{1}_{2}_{3}

Total strain distribution of the beams in _{1} in

In a similar manner, strain-shape functions for the end moments _{2} and _{3} are given by:

Then, the participation factors for the three loads

Using the scale factors
_{1}, _{2}, and _{3} are directly given by:

For the two-dimensional steel frame structure subjected to a uniformly distributed load shown in ^{8} kN/m^{2} and 6.70 × 10^{−3} m^{3}, respectively. Three FBG sensors were assumed to be attached at 3, 6, and 9 m from left-hand end of the target beam. From the strain distribution obtained from the structural analysis, the strains for FBG #1, #2, and #3 are 23.2, 266.6, and 266.6 με, respectively.

As shown in _{1} and two end moments _{2} and _{3}. Then, for the beam with span length of 15 m and the sensor locations of 3, 6, and 9 m, the participation factors in

Then, using the length of the beam _{1} = 3 _{1}, _{2}, and _{3} in Equations (^{3} and 27.4 × 10^{3} mm^{2}, respectively. The values for the loads are identical with the results from structural analysis with only a difference of 0.03 kN·m in _{2} and _{3} due to the numerical error.

To verify the performance of measurement model, a bending test of the simply supported steel beam subjected to two concentrated loads was conducted.

When the load is applied by means of a hydraulic jack, the beam deflects downward and tensile strains occur at the outer surface of the bottom flange. For each load step, to confirm the quality of measurements during the test, the measured strains from seven FBG sensors and nine ESGs are compared in

In this experimentation, two FBG sensors are required to identify the two concentrated loads using the load identification model in ^{k}

Comparing with the applied loads of 7.4 kN and 12.9 kN for the two loading steps, the summations of left and right loads are found to be very close to the ones applied from the hydraulic jack; average values of the sum of the two estimated loads are 7.427 kN with COV of 0.0180 for the first loading step and 12.84 kN with COV of 0.0087 for the second loading step.

In this paper, a strain-based load identification model for beam structures subjected to multiple loads is presented. The identification model is derived by defining the contribution of each load to the strains measured by strain sensors and the strain-shape functions for each load. In this paper, to avoid the dependency on the selection of locations of fiber Bragg grating (FBG) sensors installed at the beam structure, the deformed shape caused by the multiple loads is defined by superimposing the distribution shape of strains along the length of a beam for each load separately. The type and location of the load applied to a beam structure are necessary to define the distribution shapes. Using the deformed shape of a beam structure subjected to multiple loads, the total strain at an arbitrary point in a beam structure can be defined. Based on the results from both the numerical simulation and an experimental test, it is found that results indicate a good agreement between estimated loads based on the model and the loads applied by a hydraulic jack.

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2011-0018360).

The authors declare no conflict of interest.

Beam structure subjected to a distributed load and point loads from sub-beams.

Superposition of strain distributions caused by multi-loadings.

Numerical example for simulation. (

Experimental setup. (

Loading by hydraulic jack and loading points.

Comparison between estimated and measured strains.

Identified loads according to 20 combinations (loading step 1).

Identified loads according to 20 combinations (loading step 2).