Section List
Display section data contained in the existing fn.MCB file.

Selected List
Select section data to be imported and register them in the Selected List.

Note
If a fn.MCB is selected, all the section data contained in the existing fn.MCB file are registered in the Selected List.

Numbering Type
Specify the Import mode for section numbers.

Keep ID
Import the data keeping the same section numbers.

New ID
Assign new numbers to the imported section data.

Renumbering Section Number dialog box

Start number
Assign a new starting number for the material to be modified.

Increment
Enter the increment for numbering material property numbers.

Change element's material number
Modify a material property number. Using this option will modify the previously defined material property number. If this option is not checked, the selected material having previously defined number will become undefined and the additional user-defined material number will be created without any assigned elements.

Change Offset dialog box       

 

Offset: Specify the section Offset from the location options shown in the figure below.

Horizontal Offset: Specify the Offset in the transverse direction. "to Extreme Fiber" assigns the offset to the outer-most point. For a specific location of Offset, select 'User"and enter the distance from the "Centroid" to the desired Offset location. Unless the Offset is "Center-Center" the Horizontal Offset can be entered as the "User" type. For a tapered (non-prismatic) section, data input for the J-end also becomes activated.

Vertical Offset: Specify the Offset in the vertical direction. "to Extreme Fiber" assigns the offset to the outer-most point. For a specific location of Offset, select "User" and enter the distance from "Centroid" to the desired Offset location. Unless the Offset is "Center-Center" the Vertical Offset can be entered as the "User" type. For a tapered (non-prismatic) section, data input for the J-end also becomes activated.

Note 1

When Offset distance is specified, a positive (+) sign applies to Center-to-outward for Centroid reference and Extreme-to-inward for Extreme Fiber reference.

 

User Offset Reference: When section offset distance is specified as the "User" type, define the reference location.

Centroid: Specify the offset distance relative to the centroid of the section.

Extreme Fiber(s): Specify the offset distance relative to Left/Right & Top/Bottom.

Note 2

When User type is specified, the Offset distance and direction are entered relative to Centroid irrespective of the Center option (Centroid or Center of Section). For example, specifying "Offset: Left-Center", "Center Loc.: Center of Section" and "Horizontal offset: 0.5 " User type" will result in an Offset 0.5" to the left of the Centroid.  And if the Offset option is "Left-Center" and the Center option is Center of Section the User type for Horizontal offset becomes activated and the User type for Vertical offset becomes inactivated. The Horizontal offset defined as User type here becomes the Centroid, and the Vertical offset fixed to Center becomes the "Center of Section"

 

Note 3

When FCM Wizard is used, and "Apply the Centroid of Pier Table Section Option" is selected, the node locations of the girder will be changed as follows:

Offset: Center-Top

User Offset Reference: Extreme Fiber(s)

Vertical Offset: User, Offset Distance (i & j) = Pier Table section height-Centroid of Pier Table section

 

 

 

 

Note 4 Usage tip of Section Offset

• Internal process of section offset

   

  A beam element is defined by two nodes and a line connecting the two nodes. This line becomes a reference line representing the beam element, which usually coincides with the neutral axis of the beam element. If a section offset is assigned to a section, the neutral axis of the member shifts by the specified offset distance, and the element reference line is placed at the offset location. The reference line is used for selecting the element, assigning loads, displaying member forces, etc. The offset of the neutral axis of the member relative to the reference line in turn is reflected in analysis as shown in the figure (c) below.

   

   

  

   

• Loaded location 

   

  1. Nodal Load

   

  When an offset is assigned to a section, a nodal load remains applied to the corresponding node regardless of the offset. This results in moments due to the offset to the neutral axis as shown in the case of figure b.

   

  

  2. Element Beam Loads

   

  Element beam load is applied to the neutral axis of the element regardless of the section offset position. In the diagram below, the element beam load is applied to the neutral axis even though the section is offset from the reference line. Therefore torsional moment from the element beam load is not induced by the offset. Note however that the element beam load is displayed on the reference line as if it is applied to the reference line, but it is actually applied to the neutral axis.

   

  

   

   

• Calculation of member forces of the elements for which section offset is applied

   

  Member forces (axial force, shear force, moment & torsion) of a beam element are calculated relative to the neutral axis. This is true even when a section offset is applied. However, the member force diagrams are displayed on the reference line. This does not mean the member forces are calculated relative to the reference line.

  

  Member forces diagram when section offset is applied

• Comparison between section offset and beam end offset

   

  An offset of a section can be defined using the Beam End Offset function. For a prismatic section, a Section offset is assigned to both

  i-end and j-end identically. However, Beam End Offset can assign different offsets at i-end and j-end independently. Section offset is more useful for a tapered section as opposed to Beam End Offset as shown in the figure below.

   

  In addition, Section offset and Beam End Offset cannot be assigned simultaneously. In such a case, Section offset is ignored, and Beam End Offset only becomes effective.

   

  

  Modeling of a tapered section group when a Section offset (Center-Top) is defined

 

 

: Display the Offset specified from the Change Offset dialog box in the guide diagram of Section Data window.

Area: Cross sectional area

Asy: Effective Shear Area for shear force in the element's local y-direction

         It becomes inactive when Shear Deformation is not considered.

Asz: Effective Shear Area for shear force in the element's local z-direction

        It becomes inactive when Shear Deformation is not considered.

Ixx: Torsional Resistance about the element's local x-axis

Iyy: Moment of Inertia about the element's local y-direction

Izz: Moment of Inertia about the element's local z-direction

Cyp: Distance from the section's neutral axis to the extreme fiber of the element in the local (+)y-direction

Cym: Distance from the section's neutral axis to the extreme fiber of the element in the local (-)y-direction

Czp: Distance from the section's neutral axis to the extreme fiber of the element in the local (+)z-direction

Czm: Distance from the section's neutral axis to the extreme fiber of the element in the local (-)z-direction

Qyb: Shear Coefficient for the shear force applied in the element's local z-direction

Qzb: Shear Coefficient for the shear force applied in the element's local y-direction

Peri: O: Total perimeter of the section

Peri: I: Inside perimeter length of a hollow section

y1, z1: Distance from the section's neutral axis to the Location 1 (used for computing combined stress)

y2, z2: Distance from the section's neutral axis to the Location 2 (used for computing combined stress)

y3, z3: Distance from the section's neutral axis to the Location 3 (used for computing combined stress)

y4, z4: Distance from the section's neutral axis to the Location 4 (used for computing combined stress)

Zyy: Plastic Section Modulus about the element local y-direction

Zzz: Plastic Section Modulus about the element local z-direction

The cross-sectional area of a member is used to compute axial stiffness and stress when the member is subjected to a compression or tension force. Figure 1 illustrates the calculation procedure.

Cross-sectional areas could be reduced due to member openings and bolt or rivet holes for connections. midas does not consider such reductions. Therefore, if necessary, the user is required to modify the values using the option 2 above and his/her judgment.

Area = +dA = A1 + A2  + A3

= (300 x 15) + (573 x 10) + (320 x 12)

= 14070

<Figure 1> Example of cross-sectional area calculation

The effective shear areas of a member are used to formulate the shear stiffness in the y- and z-axis directions of the cross-section. If the effective shear areas are omitted, the shear deformations in the corresponding directions are neglected.

When midas computes the section properties by the option 1 or 3, the corresponding shear stiffness components are automatically calculated. Figure 2 outlines the calculation methods.

Asy: Effective shear area in the ECS y-axis direction

Asz: Effective shear area in the ECS z-axis direction

<Figure 2> Effective Shear Area calculations

Torsional resistance refers to the stiffness resisting torsional moments. It is expressed as

<Eq. 1>

where,

Ixx: Torsional Constant

T: Torsional moment or torque

G: Shear Modulus of Elasticity

θ : Angle of twist

The torsional stiffness expressed in Eq. 1 must not be confused with the polar moment of inertia that determines the torsional shear stresses. However, they are identical to one another in the cases of circular or thick cylindrical sections.

No general equation exists to satisfactorily calculate the torsional resistance applicable for all section types. The calculation methods widely vary for open and closed sections and thin and thick thickness sections.

For calculating the torsional resistance of an open section, an approximate method is used; the section is divided into several rectangular sub-sections and then their resistances are summed into a total resistance, Ixx, calculated by the equation below.

<Eq. 2>

 

 

for a e b

where,

Ixx: Torsional resistance of a (rectangular) sub-section

2a: Length of the longer side of a sub-section

2b: Length of the shorter side of a sub-section

Figure 3 illustrates the equation for calculating the torsional resistance of a thin walled, tube-shaped, closed section.

<Eq. 3>

 

where,

A: Area enclosed by the mid-line of the tube

ds: Infinitesimal length of thickness centerline at a given point

t: Thickness of tube at a given point

For those sections such as bridge box girders, which retain the form of thick walled tubes, the torsional stiffness can be obtained by combining the above two equations, Eq. 1 and Eq. 3.

 

Torsional resistance:

Shear stress at a given point:

Thickness of tube at a given point:

<Figure 3> Torsional resistance of a thin walled, tube-shaped, closed section

 

<Figure 4> Torsional resistance of solid sections

<Figure 5> Torsional resistance of thin walled, closed sections

<Figure 6> Torsional resistance of thick walled, open sections

<Figure 7> Torsional resistance of thin walled, open sections

 

In practice, combined sections often exist. A combined built-up section may include both closed and open sections. In such a case, the stiffness calculation is performed for each part, and their torsional stiffnesses are summed to establish the total stiffness for the built-up section.

For example, a double I-section shown in Figure 8(a) consists of a closed section in the middle and two open sections, one on each side.

<Eq. 4>

 

<Eq. 5>

 

<Eq. 6>

 

Figure 8(b) shows a built-up section made up of an I-shaped section reinforced with two web plates, forming two closed sections. In this case, the torsional resistance for the section is computed as follows:

If the torsional resistance contributed by the flange tips is negligible relative to the total section, the torsional property may be calculated solely on the basis of the outer closed section (hatched section) as expressed in Eq. 7.

<Eq. 7>

 

If the torsional resistance of the open sections is too large to ignore, then it should be included in the total resistance.

(a) Section consisted of closed and open sections

(b) Section consisted of two closed sections

<Figure 8> Torsional resistance of built-up sections

The area moment of inertia is used to compute the flexural stiffness resisting bending moments. It is calculated relative to the centroid of the section.

<Eq. 8>

 

-Area moment of inertia about the ECS z-axis

<Eq. 9>

 

: area

: distance from the reference point to the centroid of the section element in the z-axis direction

: distance from the reference point to the centroid of the section element in the y-axis direction

: first moment of area relative to the reference point in the y-axis direction

: first moment of area relative to the reference point in the z-axis direction

<Figure 9> Example of calculating area moments of inertia

The area product moment of inertia is used to compute stresses for non-symmetrical sections, which is defined as follows:

<Eq. 10>

 

Sections that have at least one axis of symmetry produce Iyz=0. Typical symmetrical sections include I, pipe, box, channel and tee shapes, which are symmetrical about at least one of their local axes, y and z. However, for non-symmetrical sections such as angle shaped sections, where Iyz`0, the area product moment of inertia should be considered for obtaining stress components.

The area product moment of inertia for an angle is calculated as shown in Figure 10.

<Figure 10> Area product moment of inertia for an angle

 

<Figure 11> Bending stress distribution of a non-symmetrical section

 

The neutral axis represents an axis along which bending stress is 0 (zero). As illustrated in the right-hand side of Figure 11, the n-axis represents the neutral axis, to which the m-axis is perpendicular. Since the bending stress is zero at the neutral axis, the direction of the neutral axis can be obtained from the relation defined as

<Eq. 11>

 

 

The following represents a general equation applied to calculate the bending stress of a section:

<Eq. 12>

 

In the case of an I shaped section, Iyz=0, hence the equation can be simplified as:

<Eq. 13>

 

where,

Iyy: Area moment of inertia about the ECS y-axis

Izz: Area moment of inertia about the ECS z-axis

Iyz: Area product moment of inertia

y: Distance from the neutral axis to the location of bending stress calculation in the ECS y-axis direction

z: Distance from the neutral axis to the location of bending stress calculation in the ECS z-axis direction

My: Bending moment about the ECS y-axis

Mz: Bending moment about the ECS z-axis

The general expressions for calculating shear stresses in the ECS y and z-axes are:

<Eq. 14>

 

<Eq. 15>

 

where,

Vy: Shear force in the ECS y-axis direction

Vz: Shear force in the ECS z-axis direction

Qy: First moment of area about the ECS y-axis

Qz: First moment of area about the ECS z-axis

by: Thickness of the section at which a shear stress is calculated, in the direction normal to the ECS z-axis

bz: Thickness of the section at which a shear stress is calculated, in the direction normal to the ECS y-axis

The first moment of area is used to compute the shear stress at a particular point on a section. It is defined as follows:

<Eq. 16>

 

<Eq. 17>

 

When a section is symmetrical about at least one of the y and z-axis, the shear stresses at a particular point are:

<Eq. 18>

 

<Eq. 19>

 

where,

Vy: Shear force acting in the ECS y-axis direction

Vz: Shear force acting in the ECS z-axis direction

Iyy: Area moment of inertia about the ECS y-axis

Izz: Area moment of inertia about the ECS z-axis

by: Thickness of the section at the point of shear stress calculation in the ECS y-axis direction

bz: Thickness of the section at the point of shear stress calculation in the ECS z-axis direction

The shear factor is used to compute the shear stress at a particular point on a section, which is obtained by dividing the first moment of area by the thickness of the section.

<Eq. 20>

  

<Eq. 21>

 

 

<Figure 12> Example of calculating a shear factor

midas calculates the stiffness for a full composite action of structural steel and reinforced concrete. Reinforcing bars are presumed to be included in the concrete section. The composite action is transformed into equivalent section properties.

The program uses the elastic moduli of the steel (Es) and concrete (Ec) defined in the SSRC79 (Structural Stability Research Council, 1979, USA) for calculating the equivalent section properties.  In addition, the Ec value is decreased by 20% in accordance with the EUROCODE 4.

- Equivalent cross-sectional area

 

- Equivalent effective shear area

 

- Equivalent area moment of inertia

 

where,

Ast1: Area of structural steel

Acon: Area of concrete

Asst1: Effective shear area of structural steel

Ascon: Effective shear area of concrete

Ist1: Area moment of inertia of structural steel

Icon: Area moment of inertia of concrete

REN: Modular ratio (elasticity modular ratio of the structural steel to the concrete, Es/Ec)

Revision of Ver.7.4.1

- Equivalent torsional coefficient

 

1. Divide the section into four quadrants.

2. Assign the positions furthermost from the centroid in each quadrant for checking stresses.

If the webs of a section are extensively sloped as in the above diagram, the points furthermost from the centroid may not be the lowest points of the section. Use caution that the stress checking positions of quadrants 3 & 4 may be selected differently from the expectation.