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Table 4 Comparative analysis for the cracking and ultimate key points—GSVATM.

From: Generalized Softened Variable Angle Truss Model for PC Beams under Torsion

Beam \( M_{Tcr,\exp } \)
(kN m)
\( M_{{Tcr,\text{th} }} \)
(kN m)
\( \frac{{M_{Tcr,\exp } }}{{M_{{Tcr,\text{th} }} }} \) \( \theta_{Tcr,\exp } \)
(º/m)
\( \theta_{{Tcr,\text{th} }} \) º/m \( \frac{{\theta_{Tcr,\exp } }}{{\theta_{{Tcr,\text{th} }} }} \) \( M_{Tu,\exp } \)
(kN m)
\( M_{{Tu,\text{th} }} \)
(kN m)
\( \frac{{M_{Tu,\exp } }}{{M_{{Tu,\text{th} }} }} \) \( \theta_{Tu,\exp } \)
(º/m)
\( \theta_{{Tu,\text{th} }} \)
(º/m)
\( \frac{{\theta_{Tu,\exp } }}{{\theta_{{Tu,\text{th} }} }} \)
P2 (Mitchell and Collins 1974) 58.0 55.4 1.05 0.14 0.09 1.55 87.1 84.5 1.03 2.80 1.86 1.50
P3 (Mitchell and Collins 1974) 41.2 44.4 0.93 0.21 0.10 2.06 55.8 71.4 0.78 3.14 2.60 1.21
P8 (Hsu and Mo 1985b) 45.2 47.6 0.95 0.24 0.21 1.13 61.8 67.4 0.92 1.89 1.66 1.14
D1 (Bernardo et al. 2013) 172.9 184.4 0.94 0.07 0.05 1.41 396.0 450.6 0.88 1.73 1.98 0.87
D2 (Bernardo et al. 2013) 184.7 178.7 1.03 0.07 0.08 0.89 447.7 434.2 1.03 1.93 1.68 1.15
PA1R (El-Degwy and McMullen 1985) 18.6 16.9 1.10 0.14 0.18 0.78 21.8 21.4 1.02 2.98 4.34 0.69
PA2 (El-Degwy and McMullen 1985) 22.8 23.1 0.99 0.61 0.23 2.71 29.3 31.5 0.93 2.87 2.85 1.01
PA3 (El-Degwy and McMullen 1985) 25.1 26.7 0.94 0.38 0.29 1.31 34.0 35.2 0.96 2.68 2.72 0.98
PA4 (El-Degwy and McMullen 1985) 26.3 28.6 0.92 0.29 0.26 1.09 37.4 40.0 0.94 2.95 2.37 1.24
PB1 (El-Degwy and McMullen 1985) 16.4 14.9 1.10 0.51 0.23 2.23 22.2 20.5 1.08 4.47 4.50 1.00
PB2 (El-Degwy and McMullen 1985) 18.9 17.0 1.11 0.43 0.23 1.87 27.5 29.7 0.93 2.75 3.24 0.85
PB3 (El-Degwy and McMullen 1985) 21.8 18.6 1.17 0.56 0.31 1.81 32.6 32.9 0.99 3.08 2.98 1.03
PB4 (El-Degwy and McMullen 1985) 24.1 22.3 1.08 0.44 0.26 1.68 37.6 36.9 1.02 2.63 2.55 1.03
PC1 (El-Degwy and McMullen 1985) 13.9 13.5 1.03 0.71 0.39 1.83 19.7 18.0 1.10 5.23 4.48 1.17
PC2 (El-Degwy and McMullen 1985) 17.2 19.3 0.89 0.33 0.22 1.54 28.6 26.5 1.08 3.38 3.46 0.98
PC3 (El-Degwy and McMullen 1985) 18.5 15.9 1.16 0.55 0.30 1.80 32.8 28.8 1.14 4.74 3.22 1.47
PC4 (El-Degwy and McMullen 1985) 21.6 22.7 0.95 0.50 0.32 1.55 38.7 33.5 1.16 3.84 2.71 1.42
H3AR (Wafa et al. 1995) 22.7 20.4 1.11 0.29 33.7 36.8 0.91 2.84
H2A (Wafa et al. 1995) 15.1 20.8 0.73 0.27 35.8 41.6 0.86 2.60
H1AR (Wafa et al. 1995) 31.6 27.7 1.14 0.25 38.4 44.0 0.87 2.34
H3B (Wafa et al. 1995) 20.7 22.6 0.91 0.37 26.4 26.8 0.98 3.31
H2B (Wafa et al. 1995) 27.1 29.2 0.93 0.37 29.5 29.1 1.01 2.90
H1B (Wafa et al. 1995) 29.9 27.8 1.07 0.37 31.3 30.7 1.02 2.85
M3A (Wafa et al. 1995) 19.6 17.9 1.09 0.36 30.0 32.6 0.92 2.87
M2A (Wafa et al. 1995) 27.0 28.8 0.94 0.44 31.9 35.3 0.91 2.58
M1A (Wafa et al. 1995) 31.5 33.1 0.95 0.33 35.4 39.1 0.91 2.37
M3B (Wafa et al. 1995) 18.3 15.5 1.18 0.38 24.7 24.6 1.01 3.48
M2B (Wafa et al. 1995) 26.2 24.5 1.07 0.41 26.2 26.3 1.00 3.11
M1B (Wafa et al. 1995) 26.8 27.5 0.97 0.43 28.9 28.6 1.01 2.88
   \( \bar{x} \) = 1.02    \( \bar{x} \) = 1.60    \( \bar{x} \) = 0.98    \( \bar{x} \) = 1.10  
   s = 0.10    s = 0.49    s = 0.09    s = 0.22  
   cv = 10.3%    cv = 30.6%    cv = 8.8%    cv = 20.3%