Analytical models
Shear strength
- \( K = 1.3 \): crimped or duoform
- \( K = 1.2 \): hooked-end
- \( K = 1.0 \): plain
\( {a \over d} \gt 2.5 \):
\( e = 1.0 \)
\( {a \over d} \le 2.5 \):
\( e = 2.5 . {d \over a} \)
Proposed equation:
\(v_u = { 1.6 . \sqrt{f_{c}} + 960 . \rho_{L} . {d \over a} . e + 8.5 . K . V_{f} . {L_{f} \over D_{f}} \over 9} \)
- \( d_{f} = 0.5 \): rounded
- \( d_{f} = 0.75 \): crimped
- \( d_{f} = 1.0 \): indented
\( F = {L_{f} \over D_{f}} . V_{f} . d_{f} \)
\(f_{spfc} = {f_{cuf} \over 20-\sqrt{F}} + 0.7 + \sqrt{F} \)
\( {a \over d} \gt 2.8 \):
\( e = 1.0 \)
\( {a \over d} \le 2.8 \):
\( e = 2.8 . {d \over a} \)
Proposed equation:
\(v_b = 0.41 . \tau . F \)
\(v_u = e . (0.24 . f_{spfc} + 80 . \rho . {d \over a}) + v_{b} \)
- \( k = 1 \): direct tension
- \( k = 2/3 \): indirect tension
- \( k = 4/9 \): flexural tension
\( f_{ct} = 0.79 . \sqrt{f_{c}} \)
Proposed equation:
\(v_u = k . f_{ct} . {d \over a}^{0.25} \)
\(\xi = { 1 \over \sqrt{ 1 + {d \over 25.d_a} } } \)
Proposed equation:
\(v_u = 0.6643 . \xi . \rho_{l}^{1/3} . [\sqrt{f_c} + 249.104 . \sqrt{ \rho_{l} \over (a/d)^5 }] \)
Proposed equation:
\( {a \over d} \ge 2.5 \):
\(v_u = 60 . (f_{c} . \rho_{l} . {1 \over a/d} )^{1/3} \)
\( {a \over d} \lt 2.5 \):
\(v_u = 60 . (f_{c} . \rho_{l} . {1 \over a/d} )^{1/3} . ({2.5 \over a/d}) \)