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 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.