Teoretické základy

Check of steel connection components (GB)

Ocel

GB (Čína)

CBFEM

Connection

Tento článek je dostupný také v dalších jazycích:

CBFEM method combines the advantages of the general Finite Element Method (FEM) and standard Component Method (CM). The stresses and internal forces calculated on the accurate CBFEM model are used in checks of all components – Bolts, preloaded bolts, and welds are checked according to GB 50017 – 2017. The plates are checked by finite element analysis. The checks of anchorage have not yet been implemented in the current version.

Code-check of steel plates according to Chinese Standard

The resulting equivalent stress (HMH, von Mises) and plastic strain are calculated on plates. When the design yield strength, f (GB 50017, Table 4.4.1–4.4.3), on the bilinear material diagram is reached, the check of the equivalent plastic strain is performed. The limit value of 5 % is suggested in Eurocode (EN 1993-1-5 App. C, Par. C8, Note 1). This value can be modified in the Code setup, but verification studies were made for this recommended value.

The plate element is divided into five layers, and elastic/plastic behavior is investigated in each of them. The program shows the worst result of all of them.

Stress may be a little bit higher than the design yield strength. The reason is the slight inclination of the plastic branch of the stress-strain diagram, which is used in the analysis to improve the stability of the calculation.

Code-check of bolts and preloaded bolts according to Chinese standard

Bolts

Bolts are checked according to GB 50017, Cl. 11.4. The tensile and shear force in each bolt is determined by finite element analysis. Prying forces are determined by finite element analysis and taken into account. Each shear plane is checked individually. The plate in the bearing is checked against the sum of shear forces at nearby planes.

Design tensile and shear strengths of a bolt; f_ub[MPa] – ultimate strength of a bolt; derived from Table 4.4.6

\(f_{ub}\) [MPa]	\(f_t^b \)	\(f_v^b\)
\(f_{ub} \le 400 \)	\(0.425 \cdot f_{ub}\)	\(0.35 \cdot f_{ub}\)
\(400<f_{ub}<830\)	\(0.42 \cdot f_{ub}\)	\(0.38 \cdot f_{ub}\)
\(830 \le f_{ub}\)	\(40/83 \cdot f_{ub}\)	\(32/83 \cdot f_{ub}\)

Bolt in tension

A bolt subject to a tensile force is designed according to Cl. 11.4.1.2 and shall satisfy:

\[ N_t \le N_t^b = A_s \cdot f_t^b \]

where:

N_t – tensile force in a bolt
N_t^b – design tension capacity
\( A_s = \frac{\pi d_e^2}{4} \) – tensile stress area of a bolt
d_e – effective diameter of a bolt at threaded section
f_t^b – design tensile strength of a bolt

Bolts in shear

A bolt subject to a shear force is designed according to Cl. 11.4.1.1 and shall satisfy:

\[ N_v \le N_v^b = A_g \cdot f_v^b \]

where:

N_v – shear force in a bolt in investigated plane
\( A_g = \frac{\pi d^2}{4} \) – gross cross-section area of a bolt
d – nominal diameter of a bolt
f_v^b – design shear strength of a bolt

Each shear plane is checked individually, i.e. number of shear planes n_v = 1.

Bolts in combined tension and shear

A bolt loaded in shear and tensile forces at the same time is designed according to Cl. 11.4.1.3 and shall satisfy:

\[ \sqrt{\left ( \frac{N_v}{N_v^b} \right ) ^2 + \left ( \frac{N_t}{N_t^b} \right ) ^2} \le 1.0 \]

where:

N_v – shear force in a bolt in investigated plane
N_t – tensile force in a bolt
N_v^b – design shear resistance of a bolt
N_t^b – design tensile resistance of a bolt

Bolts in bearing

A plate subject to a bearing force due to a bolt in shear is designed according to Cl. 11.4.1.1 and shall satisfy:

\[ N_v \le N_c^b = d\cdot t \cdot f_c^b \]

where:

N_v – shear force in acting on a plate; vector sum of shear forces in nearby planes
d – nominal bolt diameter
t – plate thickness
f_c^b – design bearing strength of a plate

Design bearing strength of a plate; f_u – ultimate strength of a plate; derived from Table 4.4.6

Preloaded bolts

High strength bolt in friction type joint is designed according to Cl. 11.4.2.

Preloaded bolts in tension

The tensile resistance of a preloaded bolt is determined as:

\[ N_t \le N_t^b = 0.8 \cdot P \]

where:

N_t – tensile force in a bolt
N_t^b – design tension capacity
P – pretension of a high strength bolt – Table 11.4.2-2

Table 11.4.2-2 – pretension of a high strength bolt P [kN]

Bolt grade	M16	M20	M22	M24	M27	M30
8.8	80	125	150	175	230	280
10.9	100	155	190	225	290	355

A preloaded bolt which is not in Table 11.4.2-2 subject to a tensile force is designed according to Cl. 11.4.1.2 and shall satisfy:

\[ N_t \le N_t^b = A_s \cdot f_t^b \]

where:

N_t – tensile force in a bolt
N_t^b – design tension capacity
\( A_s = \frac{\pi d_e^2}{4} \) – tensile stress area of a bolt
d_e – effective diameter of a bolt at threaded section
f_t^b – design tensile strength of a bolt

Preloaded bolts in shear

The design resistance of a preloaded bolt in shear is determined according to Cl. 11.4.2.1:

\[ N_v \le N_v^b = 0.9 k \mu P \]

where:

N_v – shear force in investigated plane
N_v^b – design shear resistance of a bolt
k – factor for bolt holes; k = 1 for normal holes, k = 0.85 for oversized holes, k = 0.6 for slotted holes
μ – slip coefficient at friction interface taken from Table 11.4.2-1; editable in Code setup
P = N_t^b / 0.8 – pretension of a high strength bolt for bolts which are not in Table 11.4.2-2

Each shear plane is checked individually, i.e. number of shear planes n_f = 1.

Preloaded bolts in combined tension and shear

A bolt loaded in shear and tensile forces at the same time is designed according to Cl. 11.4.2.3 and shall satisfy:

\[ \frac{N_v}{N_v^b} + \frac{N_t}{N_t^b} \le 1.0 \]

where:

N_v – shear force in investigated plane
N_t – tensile force in a bolt
N_v^b – design shear resistance of a bolt
N_t^b – design tensile resistance of a bolt

Code-check of welds according to Chinese standard

Fillet welds are checked according to GB 50017 - Chapter 11. The strength of butt welds is assumed the same as the base metal and is not checked.

Butt welds

Full penetration butt welds are expected, and their resistance is considered equal to that of the parent metal – Cl. 11.2.1.

Fillet welds

Design resistance of fillet welds is checked according to Cl. 11.2.2.2:

\[ \sigma_w = \sqrt{ \left ( \frac{\sigma_f}{\beta_f} \right ) ^2 + \tau_f^2} \le f_f^w \]

where:

σ_f – stress on the effective area of the weld perpendicular to the weld length
β_f – enlargement coefficient for design value of fillet weld strength; β_f = 1.22 for static loading and angle between fusion faces α = 90°; otherwise β_f = 1.0
τ_f – shear stress on the effective area of the weld parallel to the weld length
f_f^w – design fillet weld strength

Design fillet weld strength f_f^w for welding electrodes; derived from Table 4.4.5

Electrode	\(f_f^w\) [MPa]
E43	160
E50	200
E55	220
E60	240

Default electrodes are E43 for the weakest connected plate with f_u < 470 MPa, E50 for 470 MPa ≤ f_u < 520 MPa, and E55 for 520 MPa ≤ f_u.

The weld diagrams show stress according to the following formula:

\[ \sigma = \sqrt{ \frac{1}{\beta_f^2}(\sigma_{\perp}^2 + \tau_{\perp}^2) + \tau_{\parallel}^2 } \]

Detailing of bolts and welds according to Chinese standard

Bolts

The minimum allowable distance of bolts is checked according to Table 11.5.2.

Minimum allowable distance of bolts; d₀ – bolt hole diameter

	Minimum allowable distance
Bolt pitch	\( 3 \cdot d_0 \)
End distance parallel to load	\( 2 \cdot d_0 \)
Edge distance perpendicular to load (bearing bolt type)	\( 1.2 \cdot d_0 \)
Edge distance perpendicular to load (preloded bolt type)	\( 1.5 \cdot d_0 \)

Welds

The minimal weld size h_f is checked according to Table 11.3.5. The weld size is determined from weld throat thickness: \( h_f = \sqrt{2} \cdot h_e \).

Minimal weld size h_f

Thickness of plate [mm]	Minimum weld size [mm]
\( t \le 6 \)	3
\( 6 < t \le 12 \)	5
\( 12 < t \le 20 \)	6
\( 20<t \)	8

Code-check of concrete block according to Chinese standard

The concrete below the base plate is simulated by Winkler subsoil with uniform stiffness, which provides the contact stresses. The average stress at the bearing area used for compressive check.

Concrete in bearing

User can choose between local bearing capacity check of reinforced concrete pad (GB 50010, Equation 6.6.1-1) and plain concrete pad (GB 50010, Equation D.5.1-1).

Reinforced concrete pad

\[ F_l \le F_c = 1.35 \beta_c \beta_l f_c A_{ln} \]

Plain concrete pad

\[ F_l \le F_c = \omega \beta_l f_{cc} A_l \]

where:

F_l – compressive force
F_c – compressive resistance
β_c – strength influential coefficient of concrete; β_c = 1 for concrete grade up to C50, β_c = 0.8 for concrete grade C80; linear interpolation is used for concrete grade between C50 and C80
\( \beta_l = \sqrt{\frac{A_b}{A_l}} \) – concentration factor
A_b – concrete supporting surface which is concentric to A_l
A_l – base plate area in contact with concrete surface
A_ln – area A_l with subtracted holes in base plate for anchors
f_c – design compressive strength of concrete; GB50010, Table 4.1.4-1
f_cc = 0.85 f_c – design compressive strength of plain concrete; GB50010, Table 4.1.4-1
ω – compression load distribution factor; ω = 0.75 for uneven load distribution, ω = 1.0 for even load distribution

Transfer of shear

The shear action at the base plate is assumed to be transferred from the column to the concrete foundation by:

Friction between base plate and concrete / grout
Shear lug
Anchor bolts

Anchors

The tensile forces in anchors include prying forces and are determined by finite element analysis.

Anchors are not checked in the software.

Joint classification according to Chinese standard

Joints are classified according to joint stiffness to:

Rigid – joints with insignificant change of original angles between members,
Semirigid – joints which are assumed to have the capacity to furnish a dependable and known degree of flexural restraint,
Pinned – joints which do not develop bending moments.

There is no clear boundary between joint classes in GB 50017 and therefore, joints are classified according to the EN 1993-1-8 – Cl. 5.2.2.

Rigid – \( \frac{S_{j,ini} L_b}{E I_b} \ge k_b \)
Semirigid – \( 0.5 < \frac{S_{j,ini} L_b}{E I_b} < k_b \)
Pinned – \( \frac{S_{j,ini} L_b}{E I_b} \le 0.5 \)

where:

S_j,ini – initial stiffness of the joint; the joint stiffness is assumed linear up to the 2/3 of M_j,Rd
L_b – theoretical length of the analyzed member; set in member properties
E – Young's modulus of elasticity
I_b – moment of inertia of the analyzed member
k_b = 8 for frames where the bracing system reduces the horizontal displacement by at least 80 %; k_b = 25 for other frames, provided that in every storey K_b/K_c ≥ 0.1. The value of k_b = 25 is used unless the user sets "braced system" in Code setup.
M_j,Rd – joint design moment resistance
K_b = I_b / L_b
K_c = I_c / L_c

Capacity design according to Chinese standard

Capacity design is a part of seismic check and ensures that the joint has sufficient deformation capacity.

The connections must be able to safely transfer the force necessary to create a plastic hinge in a dissipative item. The dissipative item is selected by user alongside with the connection coefficient η_j taken from GB 50017-2017, Table 17.2.9. The connection coefficient η_j is divided between the overstrength factor γ_ov and strain-hardening factor γ_sh; η_j = γ_ovγ_sh. Strain-hardening factor γ_sh is defined by the user, and it is recommended as γ_sh = 1.1 for beam in moment resisting frame and γ_sh = 1.0 for other dissipative items. It is recommended to choose the safer η_j; e.g. η_j = 1.35 for the dissipative beam from steel grade Q345 in the moment resisting frame for the checks of both welds and bolts.