Strut-and-tie and finite element modelling of unsymmetrically-loaded deep beams
A strut-and-tie model (STM) for unsymmetrically-loaded deep beams is proposed in this paper through simplifying the unsymmetrical problem into symmetrical and anti-symmetrical problems. This analytical solution starts with derivations of principal compressive stress fields based on the theory of ela...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/162370 |
| _version_ | 1824454550534225920 |
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| author | Fan, Shengxin Zhang, Yao Ma, You-Xin Tan, Kang Hai |
| author2 | School of Civil and Environmental Engineering |
| author_facet | School of Civil and Environmental Engineering Fan, Shengxin Zhang, Yao Ma, You-Xin Tan, Kang Hai |
| author_sort | Fan, Shengxin |
| collection | NTU |
| description | A strut-and-tie model (STM) for unsymmetrically-loaded deep beams is proposed in this paper through simplifying the unsymmetrical problem into symmetrical and anti-symmetrical problems. This analytical solution starts with derivations of principal compressive stress fields based on the theory of elasticity. Furthermore, a minimum-strain-energy criterion is adopted to define the optimal STM geometry from the stress field, including the dimensions of struts and nodal zones, and strut angles. The proposed STM is validated against 140 test results, including 14 unsymmetrically-loaded deep beams and 126 symmetric deep and short beams, and finite element models (FEMs) for the 14 unsymmetrical deep beams. The FEM is also used to simulate the load-displacement relationships of unsymmetrical deep beams that could not be modelled by STM. In addition, a worked example is presented to demonstrate in detail the procedure of analysing an unsymmetrically-loaded deep beam using the proposed solution. In summary, the STM predictions are in good agreement with experimental results and FEM predictions. Therefore, the proposed STM is capable of giving accurate and consistent predictions for both symmetrical and unsymmetrical deep and short beams. |
| first_indexed | 2025-02-19T03:24:06Z |
| format | Journal Article |
| id | ntu-10356/162370 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:24:06Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1623702022-10-17T04:13:40Z Strut-and-tie and finite element modelling of unsymmetrically-loaded deep beams Fan, Shengxin Zhang, Yao Ma, You-Xin Tan, Kang Hai School of Civil and Environmental Engineering Engineering::Civil engineering Unsymmetrical Loading Deep Beams A strut-and-tie model (STM) for unsymmetrically-loaded deep beams is proposed in this paper through simplifying the unsymmetrical problem into symmetrical and anti-symmetrical problems. This analytical solution starts with derivations of principal compressive stress fields based on the theory of elasticity. Furthermore, a minimum-strain-energy criterion is adopted to define the optimal STM geometry from the stress field, including the dimensions of struts and nodal zones, and strut angles. The proposed STM is validated against 140 test results, including 14 unsymmetrically-loaded deep beams and 126 symmetric deep and short beams, and finite element models (FEMs) for the 14 unsymmetrical deep beams. The FEM is also used to simulate the load-displacement relationships of unsymmetrical deep beams that could not be modelled by STM. In addition, a worked example is presented to demonstrate in detail the procedure of analysing an unsymmetrically-loaded deep beam using the proposed solution. In summary, the STM predictions are in good agreement with experimental results and FEM predictions. Therefore, the proposed STM is capable of giving accurate and consistent predictions for both symmetrical and unsymmetrical deep and short beams. Ministry of National Development (MND) National Research Foundation (NRF) The authors wish to acknowledge the first authors scholarship from the Singapore Ministry of National Development and National Research Foundation under L2 NIC Award No. L2NICCFP1-2013-4. 2022-10-17T04:13:39Z 2022-10-17T04:13:39Z 2022 Journal Article Fan, S., Zhang, Y., Ma, Y. & Tan, K. H. (2022). Strut-and-tie and finite element modelling of unsymmetrically-loaded deep beams. Structures, 36, 805-821. https://dx.doi.org/10.1016/j.istruc.2021.12.037 2352-0124 https://hdl.handle.net/10356/162370 10.1016/j.istruc.2021.12.037 2-s2.0-85121979804 36 805 821 en L2NICCFP1-2013-4 Structures © 2021 Published by Elsevier Ltd on behalf of Institution of Structural Engineers. All rights reserved. |
| spellingShingle | Engineering::Civil engineering Unsymmetrical Loading Deep Beams Fan, Shengxin Zhang, Yao Ma, You-Xin Tan, Kang Hai Strut-and-tie and finite element modelling of unsymmetrically-loaded deep beams |
| title | Strut-and-tie and finite element modelling of unsymmetrically-loaded deep beams |
| title_full | Strut-and-tie and finite element modelling of unsymmetrically-loaded deep beams |
| title_fullStr | Strut-and-tie and finite element modelling of unsymmetrically-loaded deep beams |
| title_full_unstemmed | Strut-and-tie and finite element modelling of unsymmetrically-loaded deep beams |
| title_short | Strut-and-tie and finite element modelling of unsymmetrically-loaded deep beams |
| title_sort | strut and tie and finite element modelling of unsymmetrically loaded deep beams |
| topic | Engineering::Civil engineering Unsymmetrical Loading Deep Beams |
| url | https://hdl.handle.net/10356/162370 |
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