Table 3 Chord deformations of VATM by two-point Gauss quadrature.
From: Theoretical and Experimental Study of Effective Shear Stiffness of Reinforced ECC Columns
Member | Force | Unit load | Length | Rigidity | Deformation |
|---|---|---|---|---|---|
F | f | l | EA | Ffl/EA | |
AB | cotα | cotα | x 1 L | \( E_{s} \left[ {\frac{{A_{st} }}{2} + \frac{{\gamma \left( {1 - \xi } \right)bh}}{n}} \right] \) | \( \frac{{x_{1} L\cot^{2} \alpha }}{{E_{s} \left[ {\frac{{A_{st} }}{2} + \frac{{\gamma \left( {1 - \xi } \right)bh}}{n}} \right]}} \) |
BC | (2 − x 1)cotα/2 | (2 − x 1)cotα/2 | (1 − 2 x 1) L | \( E_{s} \left[ {\frac{{A_{st} }}{2} + \frac{{\gamma \left( {1 - \xi } \right)bh}}{n}} \right] \) | \( \frac{{L\cot^{2} \alpha \left( {1 - x_{1} } \right)^{2} \left( {1 - 2x_{1} } \right)}}{{4E_{s} \left[ {\frac{{A_{st} }}{2} + \frac{{\gamma \left( {1 - \xi } \right)bh}}{n}} \right]}} \) |
CD | cotα/2 | cotα/2 | x 1 L | \( E_{s} \left[ {\frac{{A_{st} }}{2} + \frac{{\gamma \left( {1 - \xi } \right)bh}}{n}} \right] \) | \( \frac{{x_{1} L\cot^{2} \alpha }}{{4E_{s} \left[ {\frac{{A_{st} }}{2} + \frac{{\gamma \left( {1 - \xi } \right)bh}}{n}} \right]}} \) |
EF | − cotα/2 | − cotα/2 | x 1 L | \( E_{s} \left( {\frac{{A_{st} }}{2} + \frac{\xi bh}{n}} \right) \) | \( \frac{{x_{1} L\cot^{2} \alpha }}{{4E_{s} \left( {\frac{{A_{st} }}{2} + \frac{\xi bh}{n}} \right)}} \) |
FG | − x 1cotα/2 | − x 1cotα/2 | (1 − 2 x 1) L | \( E_{s} \left( {\frac{{A_{st} }}{2} + \frac{\xi bh}{n}} \right) \) | \( \frac{{x_{1}^{2} \left( {1 - 2x_{1} } \right)L\cot^{2} \alpha }}{{4E_{s} \left( {\frac{{A_{st} }}{2} + \frac{\xi bh}{n}} \right)}} \) |
GH | 0 | 0 | x 1 L | \( E_{s} \left( {\frac{{A_{st} }}{2} + \frac{\xi bh}{n}} \right) \) | 0 |