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Identification of cross-section loads for steel beam with simple cross-sectional shape based on measured strain and its application

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Abstract

A new strain gauge layout method on the structural surface is proposed to identify the six-component loads in cross-section. Numerical simulation of a cantilever beam and an industrial case study, i.e., identification of hinge joint loads on excavator working device under actual excavating condition, are presented to demonstrate the practicability of the proposed method for industrial scale problems. The hinge joint loads deduced from the stick’s six-component cross-section loads identified by the new method were compared with the values calculated by traditional method, and the recurrence degree of stress and fatigue cumulative damage of the stick’s fatigue critical points were also compared. The maximum deviation between the actual damage of each selected measuring point and the damage caused by the identified hinge joint loads was only 1.69 %. The field test results showed that the new method could be conveniently applied with high identification accuracy for complicated actual loads.

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Abbreviations

F x :

Axial force

F y :

Shear force in horizontal plane

F z :

Shear force in vertical plane

M x :

Axial torque

M y :

Bending moment in horizontal plane

M z :

Bending moment in vertical plane

σ i :

Normal stress at i-th measuring point

T i :

Shear stress at i-th measuring point

A :

Effective area of the cross-section

A 0 :

Area enclosed by the midline in the thickness direction of each plate of the cross-section

I z :

Inertia moment of the whole cross-section to the z-axis

I y :

Inertia moment of the whole cross-section to the y-axis

y 1 :

Distance from no. 1 measuring point to z-axis

y 2 :

Distance from no. 2 measuring point to z-axis

z 3 :

Distance from no. 3 measuring point to y-axis

δ i :

Wall thickness at i-th measuring point

C i :

Sum of the widths of the webs at i-th measuring point

S y*:

Static moment of the section on one side of the y-axis to the y-axis

S z*:

Static moment of the section on one side of the z-axis to the z-axis

N :

The stress-load coefficient matrix of the cross-section

k j :

Coefficients in matrix N

ε i-0°:

Strain along the 0° directions of the i-th strain rosette

ε i-45°:

Strain along the 45° directions of the i-th strain rosette

ε i-90°:

Strain along the 0° directions of the i-th strain rosette

E :

Elastic modulus

μ :

Poisson’s ratio

b :

Width of the rectangular section

h :

Height of the rectangular section

α :

Coefficient related to the ratio h/b

F Kx2 :

Horizontal force along x2 direction at point K

F Kz2 :

Vertical force along z2 direction at point K

F Ky2 :

Lateral force along y2 direction at point K

M Kx2 :

Torque along x2 direction at point K

M Kz2 :

Bending moment along z2 direction at point K

F Fx2 :

Horizontal force along x2 direction at point F

F Fz2 :

Vertical force along z2 direction at point F

F Gx2 :

Horizontal force along x2 direction at point G

F Gz2 :

Vertical force along z2 direction at point G

F Pq :

Q-direction component of the force acting on point P

k Pq_i :

Proportional coefficient between the FPq and the stress of the i-th measuring point

M Pq :

Q-direction component of the moment acting on point P

k Pq_i’:

Proportional coefficient between the MPq and the stress of the i-th measuring point

σ i_new :

Stress of the i-th measuring point caused by all hinge joint loads identified by the new method proposed in this paper

σ i_old :

Stress of the i-th measuring point caused by all hinge joint loads identified by the traditional method

σ i_test :

Measured stresses at the i-th measuring point

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Acknowledgments

This work was supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology (Research on Key Technology of Earth-moving Machinery Fatigue Reliability (No. 2015BAF07B02)), China, and the Fundamental Research Funds for the Central Universities (No. 300102250101).

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Authors and Affiliations

  1. Key Laboratory of Highway Construction Technology and Equipment of Ministry of Education, Chang’an University, Xi’an, 710064, China

    Qingyi Xiang, Pengmin Lu & Binhua Wang

Authors
  1. Qingyi Xiang
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  2. Pengmin Lu
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  3. Binhua Wang
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Corresponding author

Correspondence to Qingyi Xiang.

Additional information

Qingyi Xiang is a lecturer in the School of Construction Machinery, Chang’an University, Xi’an, China. She received her Ph.D. in Mechanical Engineering from Chang’an University. Her research interests include load spectrum, structural strength and fatigue reliability of construction machinery, and fracture properties of welded joints.

Pengmin Lu is a Professor, Ph.D. supervisor of Chang’an University, and a Post Doctor of Beijing Jiaotong University, Beijing, China. He received his Ph.D. in Mechanical Engineering from Southwest Jiaotong University. His research interests include structural strength and fatigue reliability of construction machinery, and bridge construction machinery.

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Xiang, Q., Lu, P. & Wang, B. Identification of cross-section loads for steel beam with simple cross-sectional shape based on measured strain and its application. J Mech Sci Technol 34, 5017–5028 (2020). https://doi.org/10.1007/s12206-020-1106-3

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  • DOI: https://doi.org/10.1007/s12206-020-1106-3

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