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Datos de proyecto
Nombre del proyecto
Número del proyecto
Autor
Descripción
Fecha 19-08-2018
Norma de diseño AISC 360-10

Material
Acero A36

CON1
Conexión
Ítem
Nombre CON1
Descripción
Análisis Tensión, deformación/ Carga simplificada
Norma de diseño AISC - ASD

Elementos estructurales
β– γ- α- Desplazamiento Desplazamiento Desplazamiento
Nombre Sección Dirección Inclinación Rotación ex ey ez
[°] [°] [°] [mm] [mm] [mm]
B 1- 0,0 0,0 0,0 250 0 0
CON1
(IPE240)
M2 11 - -90,0 0,0 90,0 0 0 0
Placa
25, 160

Secciones

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Nombre Material
1 - CON1(IPE240) A36
11 - Placa 25, 160 A36

Material
Acero A36
Tornillos 7/8 A325

Tornillos / Anclajes
Diámetro fu Área bruta
Nombre Conjunto de tornillo
[mm] [MPa] [mm2]
7/8 A325 7/8 A325 22 825,0 388

Cargas
X N Vy Vz Mx My Mz
Nombre Elemento Pos.
[mm] [kN] [kN] [kN] [kNm] [kNm] [kNm]
LE1 M2 Final 0 3,0 90,0 3,0 0,0 0,0 15,3

Resultados

Resumen
Nombre Valor Estado de la verificación
Análisis 100,0% Aceptar
Placas 4,9 < 5% Aceptar
Tornillos 92,1 < 100% Aceptar

Placas
Espesor σEd εPl
Nombre Cargas Estado de la verificación
[mm] [MPa] [%]
B-bfl 1 10 LE1 158,5 4,9 Aceptar
B-tfl 1 10 LE1 152,3 1,8 Aceptar
B-w 1 6 LE1 156,7 4,0 Aceptar
M2-bfl 1 25 LE1 148,9 0,1 Aceptar
EP1 25 LE1 148,8 0,1 Aceptar
RIGIDIZAR1a 10 LE1 149,0 0,2 Aceptar
RIGIDIZAR1b 10 LE1 148,9 0,1 Aceptar
RIGIDIZAR1c 10 LE1 149,0 0,2 Aceptar
RIGIDIZAR1d 10 LE1 148,9 0,1 Aceptar
RIGIDIZAR2a 10 LE1 148,8 0,1 Aceptar
RIGIDIZAR2b 10 LE1 148,8 0,1 Aceptar
Datos de diseño
fy εlim
Material
[MPa] [1e-4]
A36 248,2 500,0
Explicación del símbolo
Símbolo Explicación del símbolo
εPl Deformación
σEd Ec. tensión

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Verificación de deformación, LE1

Tensión equivalente, LE1

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Tornillos
Ft V Utt Uts Utts
Nombre Cargas Estado
[kN] [kN] [%] [%] [%]
B1 LE1 99,7 18,4 82,9 27,9 82,9 Aceptar

B2 LE1 48,5 26,8 40,3 40,4 43,4 Aceptar

B3 LE1 110,7 16,9 92,1 25,5 92,1 Aceptar

B4 LE1 76,5 28,2 63,6 42,6 70,0 Aceptar

Datos de diseño
Rn/ΩTracción Rn/ΩCortante Rn/ΩAplastamiento
Nombre
[kN] [kN] [kN]
7/8 A325 - 1 120,3 72,2 66,2
Explicación del símbolo
Símbolo Explicación del símbolo
Ft Fuerza de tracción
V Resultante de las fuerzas cortantes Vy, Vz en el tornillo.
Rn/ΩTracción Resistencia de los tornillos a tracción AISC 360-10 tabla J3.2
Rn/ΩCortante Resistencia de los tornillos a cortante AISC 360-10 tabla J3.2
Rn/ΩAplastamiento Resistencia al desgarro de la placa AISC 360-10 J3.10
Utt Utilización a tracción
Uts Utilización a cortante
φVcbg Fallo de resistencia del borde de horimgón, AISC Guia de diseño 01
Utts Interacción de la tracción y el cortante AISC 360-10 J3.7

Configuración de la norma
Ítem Valor Unidad Referencia
Coeficiente de fricción 0,25 -
Coeficiente de fricción 0,30 -
Deformación plástica límite 0,05 -
Evaluación de la tensión de la soldadura Aplicar plasticidad en las
soldaduras
Detallado No
Distancia entre tornillos [d] 2,66 - AISC 360-10 -
J3
Distancia entre tornillos y el borde [d] 1,25 -
Resistencia de rotura del cono de hormigón - Sí
ETAG

Theoretical Background
CBFEM versus Components method
The weak point of standard Component method is in analyzing of internal forces and stress in a joint. CBFEM replaces specific analysis of
internal forces in joint with general FEA.

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Check methods of specific components like bolts or welds are done according to standard Component method (Eurocode).
For the fasteners – bolts and welds – special FEM components had to be developed to model the welds and bolts behaviour in joint. All parts of
1D members and all additional plates are modelled as plate/walls. These elements are made of steel (metal in general) and the behaviour of this
material is significantly nonlinear.
The real stress-strain diagram of steel is replaced by the ideal plastic material for design purposes in building practice. The advantage of ideal
plastic material is, that only yield strength and modulus of elasticity must be known to describe the material curve. The granted ductility of
construction steel is 15 %. The real usable value of limit plastic strain is 5% for ordinary design (1993-1-5 appendix C paragraph C.8 note 1).
The stress in steel cannot exceed the yield strength when using the ideal elastic-plastic stress-strain diagram.

Real tension curve and the ideal elastic-plastic diagram of material

CBFEM method tries to create to model the real state precisely. The analysis plate/walls are not interconnected, no intersections are generated
between them, unlike it is used to when modelling structures and buildings. Mesh of finite elements is generated on each individual plate
independently on mesh of other plates.
Welds are modelled as special massless force interpolation constrains, which ensure the connection between the edge of one plate and the
surface or edge of the other plate.
This unique calculation model of bolt provides very good results – both for the point of view of precision and of the analysis speed. The method
protected by patent.
The steel base plate is placed loosely on the concrete foundation. It is a contact element in the analysis model – the connection resists fully to
compression, but does not resist to tension.

Stress-strain diagram of contact between the concrete block and the base plate

Two approaches of modelling welds are implemented.

The first option of weld model between plates is direct merge of meshes of welded plates. The load is transmitted through a force-deformation
constrains to opposite plate. This model does not respect the stiffness of the weld and the stress distribution is conservative. Stress peaks, which
appear at the end of plate edges, in corners and rounding, govern the resistance along the whole length of the weld. To eliminate the effect of
stress peaks three methods for evaluation of the weld can be chosen:

• Maximal stress (conservative)

• Average stress on weld
• Linear interpolation along weld

The second approach uses an improved weld model. A special elastoplastic element is added between the plates. The element respects the weld
throat thickness, position and orientation. Ideal plastic model is used and the plasticity state is controlled by stresses in the weld throat section.
The stress peaks are redistributed along the longer part of the weld length.

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Bolted connection consists of two or more clasped plates and one or more bolts. Plates are placed loosely on each other.
A contact element is inserted between plates in the analysis model, which acts only in compression. No forces are carried in tension.

Shear force is taken by bearing. Special model for its transferring in the force direction only is implemented. IDEA StatiCa Connection can check
bolts for interaction of shear and tension. The bolt behavior is implemented according following picture.

Bolt - tension

Symbols explanation:

• K – linear stiffness of bolt,

• Kp – stiffness of bolt at plastic branch,
• Flt – limit force for linear behaviour of bolt,
• Ft,Rd – limit bolt resistance,
• ul – limit deformation of bolt.

Bolt - interaction of shear and tension

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The concrete block in CBFEM is modelled using Winkler-Pasternak subsoil model. The stiffness of subsoil is determined using modulus of
elasticity of concrete and effective height of subsoil. The concrete block is not designed by CBFEM method. Only the minimal dimension of block
under the base plate is determined to avoid the concrete cone breakout.

Loads
End forces of member of the frame analysis model are transferred to the ends of member segments. Eccentricities of members caused by the
joint design are respected during transfer.
The analysis model created by CBFEM method corresponds to the real joint very precisely, whereas the analysis of internal forces is performed
on very idealised 3D FEM 1D model, where individual beams are modelled using centrelines and the joints are modelled using immaterial nodes.

Real shape and theoretical 3D FEM model of joint of vertical column and horizontal beam

Internal forces are analysed using 1D members in 3D model. There is an example of courses of internal forces in the following picture.

Course of bending moment and shear force on horizontal beam. M and V are the end forces at joint.

The effects caused by member on the joint are important to design the joint (connection). The effects are illustrated in the following picture.

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Effects of member on the joint in 1D members model and CBFEM model. CBFEM model is drawn in dark color.

Moment M and force V act in theoretical joint. The point of theoretical joint does not exist ni CBFEM model, thus the load cannot be applied here.
The model must be loaded by actions M and V, which have to be transferred to the end of segment in the distance r.
Mc = M – V . r
Vc = V
In CBFEM model, the end section of segment is loaded by moment Mc and force Vc.

Welds

Fillet welds
The design strength, ΦRn and the allowable strength, Rn/Ω of welded joints are evaluated in connection weld check.
Φ = 0.75 (LRFD)
Ω = 2.00 (ASD)
Available strength of welded joints is evaluated according to AISC 360-10 table J2,5:
Rn = Fnw Awe
Fnw = 0.60FEXX (1.0 + 0.50 sin 1.5 Θ)
where

• Fnw - nominal stress of weld material,

• Awe - effective area of the weld,
• FEXX - electrode classification number, i.e., minimum specified tensile strength,
• Θ - angle of loading measured from the weld longitudinal axis, degrees.

For end-loaded fillet welds with a length up to 100 times the weld size, it is permitted to take the effective length equal to the actual length. When
the length of the end-loaded fillet weld exceeds 100 times the weld size, the effective length shall be determined by multiplying the actual length
by the reduction factor, β, determined as follows:
β = 1.2 - 0.002 (l / w)
where

• l - weld length,
• w - size of weld leg.

When the length of the weld exceeds 300 times the leg size, w, the effective length is taken as 180w.

CJP groove welds

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AISC Specification Table J2.5 identifies four loading conditions that might be associated with JP groove welds, and shows that the strength of the
joint is either controlled by the base metal or that the loads need not be considered in the design of the welds connecting the parts. Accordingly,
when CJP groove welds are made with matching-strength filler metal, the strength of a connection is governed or controlled by the base metal,
and no checks on the weld strength are required.

Bolts

Tensile and shear strength of bolts

The design tensile or shear strength, ΦRn, and the allowable tensile or shear strength, Rn/Ω of a snug-tightened bolt is determined according to
the limit states of tension rupture and shear rupture as follows:
Rn = Fn Ab
Φ = 0.75 (LRFD)
Ω = 2.00 (ASD)
where

• Ab - nominal unthreaded body area of bolt or threaded part, in2 (mm2)

• Fn - nominal tensile stress, Fnt, or shear stress, Fnv, from Table J3.2, ksi (MPa)

The required tensile strength includes any tension resulting from prying action produced by deformation of the connected parts.

Combined Tension and shear in bearing type connection

The available tensile strength of a bolt subjected to combined tension and shear is determined according to the limit states of tension and shear
rupture as follows:
Rn = F'nt Ab (AISC 360-10 J3-2)
Φ = 0.75 (LRFD)
Ω = 2.00 (ASD)
Fn't = 1,3Fnt - frv Fnt/ ΦFnv (AISC 360-10 J3-3a LRFD)
Fn′t = 1,3Fnt - frv Ω Fnt/Fnv (AISC 360-10 J3-3b ASD)
where

• Fn′t - nominal tensile stress modified to include the effects of shear stress
• Fnt - nominal tensile stress from AISC 360-10 Table J3.2
• Fnv - nominal shear stress from AISC 360-10 Table J3.2
• frv - required shear stress using LRFD or ASD load combinations. The available shear stress of the fastener shall be equal or exceed the
required shear stress, frv.

Bearing strength in bolt holes

The available bearing strength, ΦRn and Rn/Ω at bolt holes is determined for the limit state of bearing as follows:
Φ = 0.75 (LRFD)
Ω = 2.00 (ASD)
The nominal bearing strength of the connected material, Rn, is determined as follows:
For a bolt in a connection with standard, oversized and short-slotted holes, independent of the direction of loading, or a long-slotted hole with the
slot parallel to the direction of the bearing force

When deformation at the bolt hole at service load is a design consideration

Rn = 1.2 lc t Fu ≤ 2.4 d t Fu (AISC 360-10 J3-6a)

When deformation at the bolt hole at service load is not a design consideration
Rn = 1.5 lc t Fu ≤ 3.0 d t Fu (AISC 360-10 J3-6b)

where

• Fu - specified minimum tensile strength of the connected material,

• d - nominal bolt diameter,
• lc - clear distance, in the direction of the force, between the edge of the hole and the edge of the adjacent hole or edge of the material,
• t - thickness of connected material.

Preloaded bolts
The design slip resistance of a preloaded class A325 or A490 bolt without of effect of tensile force, Ft,Ed.
Preloading force to be used AISC 360-10 tab. J3.1.
Tb = 0,7 fub As
Design slip resistance per bolt AISC 360-10 par. 3.8
Rn = 1.13 μ Tb Ns
Utilisation in shear [%]:
Uts = V / Rn where

• As - tensile stress area of the bolt,

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• fub - ultimate tensile strength,

• μ - slip factor obtained,
• Ns - number of the friction surfaces. Check is calculated for each friction surface separately.
• V - shear force.

Anchors
Concrete Capacity Design (CCD). In the CCD method, the concrete cone is considered to be formed at an angle of approximately 34° (1 to 1.5
slope). For simplification, the cone is considered to be square rather than round in plan. The concrete breakout stress in the CCD method is
considered to decrease with an increase in size of the breakout surface. Consequently, the increase in strength of the breakout in the CCD
method is proportional to the embedment depth to the power of 1.5.
Φ Ncbg = Φ ψ3 24 √fc hef1,5 An/An0 for hef < 11 in
Φ Ncbg = Φ ψ3 16 √fc hef1,66 An/An0 for hef >= 11 in
where

• Φ = 0.70,
• ψ3 = 1.25 considering the concrete to be uncracked at service loads, otherwise =1.0,
• hef - depth of embedment,
• An - concrete breakout cone area for group,
• An0 - concrete breakout cone area for single anchor.

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