Bond of embedded steel reinforcement

structuralcodes.codes.mc2010.K_tr(n_t: float, A_st: float, n_b: float, phi: float, s_t: float) → float[source]

Coefficient accounting for transverse stresses, K_tr.

fib Model Code 2010, Eq. (6.1-6).

Parameters:

  • n_t (float) – Number of legs of confining reinforcement crossing a potential splitting failure surface at a section.

  • A_st (float) – Cross-sectional area of one leg of a confining bar in mm^2.

  • n_b (float) – Number of anchored bars or pairs of lapped bars in potential splitting surface.

  • phi (float) – Nominal bar diameter in mm.

  • s_t (float) – Longitudnal spacing of confining reinforcement in mm.

Returns:

K_tr as value.

Return type:

float

structuralcodes.codes.mc2010.eta_2(bond: Literal['good', 'other']) → float[source]

Bond coefficient eta_2.

fib Model Code 2010, Eq. (6.1-5).

Parameters:

bond (str) – Bond condition according to Subsection 6.1.3.2. Input must be ‘good’ or ‘other’.

Returns:

eta_2 value.

Return type:

float

Raises:

ValueError – If a proper value for ‘bond’ is not input.

structuralcodes.codes.mc2010.f_stm(f_cm: float, phi: float, l_b: float, c_min: float, c_max: float, k_m: float, K_tr: float) → float[source]

Reinforcement stress, f_stm.

fib Model Code 2010, Eq. (6.1-19).

Parameters:

  • f_cm (float) – Mean cylinder concrete compressive strength in MPa.

  • phi (float) – Nominal bar diameter in mm.

  • l_b (float) – Bond length in mm.

  • c_min (float) – Parameter shown in Figure 6.1-2.

  • c_max (float) – Parameter shown in Figure 6.1-2.

  • k_m (float) – Parameter shown in Figure 6.1-3.

  • K_tr (float) – Parameter calculated with Eq.(6.1-6).

Returns:

f_stm in MPa.

Return type:

float

Raises:

  • UserWarning – If not 15 MPa < f_cm < 110 MPa.

  • UserWarning – If not 0.5 < c_min / phi < 3.5.

  • UserWarning – If not 1.0 < c_max / c_min < 5.0.

  • UserWarning – If not K_tr <= 0.05.

structuralcodes.codes.mc2010.s_1(bond: Literal['good', 'other']) → float[source]

Slip at maximum bond stress, s_1.

fib Model Code 2010, Table 6.1-1.

Parameters:

bond (str) – Bond condition according to Subsection 6.1.3.2. Must be ‘good’ or ‘other’.

Returns:

s_1 in mm.

Return type:

float

Raises:

ValueError – If a proper value for ‘bond’ is not input.

structuralcodes.codes.mc2010.s_2(bond: Literal['good', 'other']) → float[source]

s_2 according to Table 6.1-1.

Parameters:

bond (str) – Bond condition according to Subsection 6.1.3.2. Must be ‘good’ or ‘other’.

Returns:

s_2 in mm.

Return type:

float

Raises:

ValueError – If a proper value for ‘bond’ is not input.

structuralcodes.codes.mc2010.s_3(failmod: Literal['PO', 'SP'], bond: Literal['good', 'other'], confinement: Literal['unconfined', 'stirrups'], c_clear: float, s_1: float) → float[source]

s_3 according to Table 6.1-1.

Parameters:

  • failmod (str) – Failure mode. Must be “PO” for Pull-out of “SP” for Splitting.

  • bond (str) – Bond condition according to Subsection 6.1.3.2. Must be ‘Good’ or ‘Other’.

  • confinement (str) – Confinement conditions. Must be “Unconfined” or “Stirrups”

  • c_clear (float) – Clear distance between ribs in mm.

  • s_1 (float) – s_1 according to Table 6.1-1 columns 1 and 2 for Pull-out failure.

Returns:

s_3 in mm.

Return type:

float

Raises:

  • ValueError – If a proper value for ‘failmod’ is not input.

  • ValueError – If a proper value for ‘bond’ is not input.

  • ValueError – If a proper value for ‘confinement’ is not input.

structuralcodes.codes.mc2010.s_tau_bu_split(tau_bmax: float, tau_bu_split: float, alpha: float, s_1: float) → float[source]

Calculates the slip at tau_bu_split by rewriting Eq. 6.1-1 to solve for s and substituting tau_bu_split for tau_b.

Parameters:

  • tau_bmax (float) – Maximum bond stress according to Table 6.1-1.

  • tau_bu_split (float) – Concrete bond stress at splitting failure.

  • alpha (float) – Parameter in Eq. 6.1-1. Alpha is 0.4 in Table 6.1-1.

  • s_1 (float) – s_1 according to Table 6.1-1.

Returns:

Slip at tau_bu_split in mm.

Return type:

float

structuralcodes.codes.mc2010.tau_bmax(bond: Literal['good', 'other'], f_cm: float) → float[source]

Maximum bond stress tau_bmax.

fib Model Code 2010, Table 6.1-1.

Parameters:

  • bond (str) – Bond condition according to Subsection 6.1.3.2. Must be ‘good’ or ‘other’.

  • f_cm (float) – Mean cylinder concrete compressive strength in MPa.

Returns:

tau_bmax in MPa.

Return type:

float

Raises:

ValueError – If a proper value for ‘bond’ is not input.

structuralcodes.codes.mc2010.tau_bu_split(eta_2: float, f_cm: float, phi: float, c_min: float, c_max: float, k_m: float, K_tr: float) → float[source]

Maximum bond stress in case of splitting failure.

fib Model Code 2010, Eq. (6.1-5).

Parameters:

  • eta_2 (float) – Parameter based on bond condition. 1.0 for ‘good’ bond condition and 0.7 for ‘other’ conditions.

  • f_cm (float) – Mean cylinder concrete compressive strength in MPa.

  • phi (float) – Nominal bar diameter in mm.

  • c_min (float) – Parameter according to MC2010 Figure 6.1-2.

  • c_max (float) – Parameter according to MC2010 Figure 6.1-2.

  • k_m (float) – Parameter according to MC2010 Figure 6.1-3.

  • K_tr (float) – To be calculated with MC2010 Eq.(6.1-6).

Returns:

tau_bu_split in MPa.

Return type:

float

structuralcodes.codes.mc2010.tau_yield(f_y: float, l_b: float, phi: float) → float[source]

Calculates the bond stress at yield of the reinforcement bar based on a uniform bond stress over l_b.

The bond stress at yield is a limit for: - tau_bmax, given with eps_s < eps_s,y in Table 6.1-1. - tau_bu_split, explicitly stated for Eq. 6.1-19.

Parameters:

  • f_y (float) – Reinforcement bar yield stress in MPa.

  • l_b (float) – Bond length with uniform bond stress assumed in mm.

  • phi (float) – Nominal bar diameter in mm.

Returns:

Bond stress at yield of rebar in MPa.

Return type:

float