check_local_buckling_resistance_about_zz_axis: Perform check #3, calculating the local buckling resistance...

In shadowboxingskills/civilR: Civil Engineering R package

Description

Calculate the local buckling resistance of member about minor z-z axis, based on EC3 Approach.

L_e=kL_{ch}

[mm] where L is the critical length for buckling about minor axis z-z Steps of the check performed for laced struts:

1. Plastic resistance of the cross-section to compression [kN]

   N_{pl,R_d,ch}= 2(A \, fy)

2. The Euler buckling load [kN]

   N_{cr,ch}=\frac{π^2 \, E \, I_{zz}}{{L_e}^2}

3. Relative slenderness [dimensionless]

   \bar{λ_{ch}} = √{ \frac{N_{pl,R_d,ch}}{N_{cr,ch}} }

4. Calculate Φ_{ch} parameter for slenderness reduction factor

   Φ_{ch} = 0.5 ≤ft[ 1 + α ≤ft( \bar{λ_{ch}}-0.2 \right) + {\bar{λ_{ch}}}^2 \right]

5. Slenderness reduction factor [dimensionless]

   X_{ch} = \frac{1}{ Φ_{ch}+√{{Φ_{ch}}^2-{\bar{λ_{ch}}}^2} }

6. Output overall buckling resistance of the struts about z-z minor axis [kN]

   N_{b,R_d,ch}=X_{ch} \, N_{pl,R_d,ch}

The partial factors γ_M that are applied to resistance of members to instability: γ_{M_1} = 1

Usage

check_local_buckling_resistance_about_zz_axis(
  trial_member_size,
  member_type,
  steel_grade,
  k,
  Lch,
  E,
  list_reference_tables
)

Arguments

trial_member_size	Trial member size
member_type	member_type, categorical: 'UC' or 'UB'
steel_grade	steel_grade [N/{mm}^2], categorical: 'S355' or 'S275'
k	Coefficient [dimensionless]
Lch	Length of chord [mm]
E	Young's Modulus of Elasticity [GPa]
list_reference_tables	List of reference tables

Value

• N_{b,Rd,X} Local buckling resistance of struts about z-z axis [kN]

• f_y

• N_{pl,R_d}

• N_{cr}

• {\bar{λ}}

• α_{yy}

• X

shadowboxingskills/civilR documentation built on Oct. 24, 2020, 12:22 p.m.