Column base plate design according to EN 1993-1-1: 2005

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Column base plate are flat plates of steel used in composite construction to connect steel column (stanchion) to a reinforced concrete foundation. Steel stanchions usually consist of sharp edges. Thus, if they are connected directly to the reinforced concrete foundation, they can cause sinking effect on the concrete which can lead it to crack or crack. The provision of high strength base plate is to ensure that the load from column is dispersed over a wide area of the base plate before being uniformly distributed over the reinforced concrete foundation (See Figure 1).

Prior to the design of base plate, the load to be carried by the base plate which include the axial load, the shear force and the moment are accessed and this formed the parameters of the design. These parameters are used to get adequate size of base plate to support such column. A typical design of base plate based on EN 1993-1-1:2005 is presented below. The design parameters were assigned arbitrarily.

Design forces

Design axial force (compression);   N_Ed = 300 kN

Design shear force;   V_Ed = 43 kN

Design moment;   M_Ed = 35 kNm

Column Details

Column section;   UKC 254x254x73

Depth;   D = 254.1 mm

Width;   B = 254.6 mm

Flange thickness;   T = 14.2 mm

Web thickness;   t = 8.6 mm

Base plate details

Length;   h_p = 500 mm

Width;   b_p = 500 mm

Thickness;   t_p = 15 mm

Column eccentricity in x-axis;   e_bpx = 0 mm

Anchor details

Number of anchors LHS;   n₁ = 2

Edge distance in  x-axis;   e_x1 = 50 mm

Edge distance in y-axis;   e_y1 = 50 mm

Number of anchors RHS;   n₂ = 2

Edge distance in x-axis;   e_x2 = 50 mm

Edge distance in the y-axis;   e_y2 = 50 mm

Anchor diameter;   d_a,b = 24 mm

Foundation details

Foundation depth;   t_fnd = 500 mm

Concrete details

Concrete strength class;   C25/30

Characteristic compressive cylinder strength;    f_ck = 25 N/mm²

Characteristic compressive cube strength;   f_ck,cube = 30 N/mm²

Partial factor for concrete;   g_c = 1.50

Compressive strength coefficient;   a_cc = 0.85

Design compressive concrete strength;   f_cd = a_cc ´ (f_ck / g_c) = 14.17 N/mm²

Steel details

Base plate steel grade;   S275

Base plate nominal yield strength;   f_{yp_plt} = 275 N/mm²

Base plate nominal ultimate tensile strength;   f_{u_plt} = 410 N/mm²

Column steel grade;    S275

Column nominal yield strength;   f_{yp_col} = 275 N/mm²

Column nominal ultimate tensile strength;   f_{u_col} = 410 N/mm²

Partial safety factor cross sections;   g_M0 = 1.00

Partial safety factor welds;   g_M2 = 1.25

Tension and compression lever arms

LHS compressive lever arm – Fig 6.18;   z_C,l = (D – T) / 2 = 120 mm

RHS compressive lever arm – Fig 6.18;    z_C,r = (D – T) / 2 = 120 mm

LHS tension lever arm – Fig 6.18;    z_T,l = h_p / 2 + e_bpx – e_x1 = 200 mm

RHS tension lever arm – Fig 6.18;   z_T,r = h_p / 2 – e_bpx – e_x2 = 200 mm

Design forces in T-stubs

Force in left hand T-stub;   N_L,T = N_Ed ´ z_C,r / (z_C,l + z_C,r) – M_Ed / (z_C,l + z_C,r) = 4.1 kN; (Comp)

Force in right hand T-stub;    N_R,T = N_Ed ´ z_C,l / (z_C,l + z_C,r) + M_Ed / (z_C,l + z_C,r) = 295.9 kN; (Comp)

Foundation bearing strength under left hand flange – EN1992-1-1 Section 6.7

Left hand flange

Additional bearing width – Eqn 6.5;    c_LF = t_p ´ Ö(f_{yp_plt} / (3 ´ f_jd,LF ´ g_M0)) = 29 mm

Effective width of T-stub flange;    b_eff1,LF = 72.2 mm

Effective length of T-Stub flange;    l_eff1,LF = 312.6 mm

Loaded area;    A_c0,LF = b_eff1,LF ´ l_eff1,LF = 22557 mm²

Design distribution width;   b_eff2,LF = 187.6 mm

Design distribution length;   l_eff2,LF = 812.6 mm

Maximum design distribution area;    A_c1,LF = b_eff2,LF ´ l_eff2,LF = 152445 mm²

Concentrated design resistance force;    F_Rdu,LF = Min(A_c0,LF ´ f_cd ´ Ö(A_c1,LF / A_c0,LF), 3 ´ f_cd ´ A_c0,LF) = 830.7 kN

Foundation joint material coefficient;    b_j = 0.67

Design bearing strength of the joint – Eqn 6.6;    f_jd,LF = b_j ´ F_Rdu,LF / (b_eff1,LF ´ l_eff1,LF) = 24.55 N/mm²

Foundation bearing strength under right hand flange – EN1992-1-1 Section 6.7

Additional bearing width – Eqn 6.5;    c_RF = t_p ´ Ö(f_{yp_plt} / (3 ´ f_jd,RF ´ g_M0)) = 29 mm

Effective width of T-stub flange;    b_eff1,RF = 72.2 mm

Effective length of T-Stub flange;   l_eff1,RF = 312.6 mm

Loaded area;   A_c0,RF = b_eff1,RF ´ l_eff1,RF = 22557 mm²

Design distribution width;    b_eff2,RF = 187.6 mm

Design distribution length;    l_eff2,RF = 812.6 mm

Maximum design distribution area;   A_c1,RF = b_eff2,RF ´ l_eff2,RF = 152445 mm²

Concentrated design resistance force;    F_Rdu,RF = Min(A_c0,RF ´ f_cd ´ Ö(A_c1,RF / A_c0,RF), 3 ´ f_cd ´ A_c0,RF) = 830.7 kN

Foundation joint material coefficient;   b_j = 0.67

Design bearing strength of the joint – Eqn 6.6;   f_jd,RF = b_j ´ F_Rdu,RF / (b_eff1,RF ´ l_eff1,RF) = 24.55 N/mm²

Equivalent T-stub in compression under right hand flange – Section 6.2.5

Design compression resistance of T-stub flange;   F_C,Rd2 = f_jd,RF ´ b_eff1,RF ´ l_eff1,RF = 553.8 kN

Equivalent T-stub in compression under left hand flange – Section 6.2.5

Design compression resistance of T-stub flange;   F_C,Rd1 = f_jd,LF ´ b_eff1,LF ´ l_eff1,LF = 553.8 kN

Concrete in compression under right hand flange – Section 6.2.6.9

Design resistance of concrete in compression;   F_c,pl,Rd2 = F_C,Rd2 = 553.8 kN

Concrete in compression under left hand flange – Section 6.2.6.9

Design resistance of concrete in compression;   F_c,pl,Rd1 = F_C,Rd1 = 553.8 kN

Bending resistance of column – EN1993-1-1 Section 6.2.5

Design resistance for bending – Cls 6.2.5(2);   M_c,Rd = M_pl,Rd = W_pl,y ´ f_{yp_col} / g_M0 = 272.8 kNm

Beam flange and web in compression – Section 6.2.6.7

Design compression resistance of flange – Eqn 6.21;   F_c,fc,Rd = M_c,Rd / (D – T) = 1137.2 kN

Column bases subjected to axial forces and bending moments – Section 6.2.8.3

Design compression resistance LHS of joint;   F_C,l,Rd = Min(F_c,pl,Rd1, F_c,fc,Rd) = 553.8 kN

Design compression resistance RHS of joint;   F_C,r,Rd = Min(F_c,pl,Rd2, F_c,fc,Rd) = 553.8 kN

Design moment resistance of column base

Relative eccentricity of load – Tbl 6.7;   e = M_Ed / (-N_Ed) = -116.7 mm

Loading type – Tbl 6.7;   Left side compression & Right side compression

Lever arm – Tbl 6.7;   z = z_C,l + z_C,r= 239.9 mm

Design moment resistance – Tbl 6.7;   M_j,Rd = Min(Abs(-F_C,l,Rd ´ z / (z_C,r / e + 1)), Abs(-F_C,r,Rd ´ z / (z_C,l / e – 1))) = 65.5 kNm

PASS – Design moment of resistance exceeds applied moment

Frictional shear resistance

Base plate friction coefficient;   C_f,d = 0.2

Design frictional shear resistance;   F_f,Rd = C_f,d ´ (N_L,T + N_R,T) = 60 kN

PASS – Design frictional resistance exceeds applied shear load

Shear weld

Force in shear weld;   F_w,v,Ed = 43 kN

Weld leg length;   s_w = 6 mm

Weld throat size;   a_w = 1 / Ö(2) ´ s_w = 4.2 mm

Length of weld;   L_w,v = 2 ´ (D – 2 ´ (T + r)) = 400.6 mm

Correlation factor for fillet welds – Table 4.1;   b_w = 0.85

Design shear strength – Cls 4.5.3.3(3);   f_vw,d = f_{u_plt} / (Ö(3) ´ b_w ´ g_M2) = 222.8 N/mm²

Design resistance per unit length – Cls 4.5.3.3(2);   f_w,Rd = f_vw,d ´ a_w = 945.2 N/mm

Design resistance;   F_w,v,Rd = f_w,Rd ´ L_w,v = 378.7 kN

PASS – Available strength of weld exceeds force in weld

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