## Function

- Enter the sectional properties for the following structural elements: Truss, Tension-only, Compression-only, Cable, Gap, Hook, and Beam Element.
- In the "Tapered" tab, you can define the section properties of a tapered section where the sizes vary at both ends.

## Call

From the main menu, select **[Properties] tab > [Section Properties] group > [Section Properties]**** > [Tapered]**

## Input

Section(Tapered) dialog box

### Input Section Shape

**Section Shape List** : Applicable tapered section shapes are shown below. For PSC, Composite Type or General Section of Value type, pre-defined sections can be brought in from the Section DB.

**DB/User** : All sections except for the R-Octagon section

**Value** : All sections except for the R-Octagon section

**PSC** : All PSC Type sections

**Composite** : Composite sections (Steel-Box, Steel-I, PSC-I, PSC-T & General section)

**Value** : Assign value when the user directly enters the section stiffness data.

Enter the section dimensions for section-i and j separately and click **Calculate Stiffness**. Then, the user may modify the auto-calculated stiffness data or directly enter the stiffness data without entering the section dimensions.

**User** : Enter the main dimensions of standardized section shapes.

**DB** : Select the sections from the DB of the standard sections for a country.

**KS** : Korean Industrial Standards

**AISC2K(US)** : American Institute of Steel Construction, 2000 (US Unit : lb, in)

**AISC2K(SI)** : American Institute of Steel Construction, 2000 (SI Unit : kN, m)

**AISC** : American Institute of Steel Construction

**CISC02(US)** : Canadian Institute of Steel Construction (US Unit : lb, in)

**CISC02(SI)** : Canadian Institute of Steel Construction (SI Unit : kN, m)

**BS** : British Standards

**DIN(S)** : Deutshes Institut Fur Normung e.v.

**JIS** : Japanese Industrial Standards

**JIS2K** : Japanese Industrial Standards 2000

**GB-YB** : Guojia Biao Zhun-Yejin Bu Biao Zhunteel Construction, 2000 (Metric Unit :N, m)

**GB-YB** : Guojia Biao Zhun-Yejin Bu Biao Zhun(2005)

**Pacific(SI)** : Bentley Pacific Standards (SI Unit : kN, m)

**IS84** : Indian Standards

**CNS91** : Taiwan Standards

### Section-i, Section-j

Enter directly each section name corresponding to the starting section-i and the ending section-j or select the desired DB from the section list to describe the tapered section. When the section names are directly entered, they must correspond to the DB section name format.

Ex) KS, JIS : H 400X200X8/13, AISC : W36X280, CISC : HP310x110, BS : UB 406x178x54, DIN : HD400x288

### y Axis Variation, z Axis Variation

**y Axis Variation** : Dimensional variation affects the moment of inertia about the element local y-axis along the length.

**z Axis Variation** : Dimensional variation affects the moment of inertia about the element local z-axis along the length.

**Linear** : linear variation along the element local x-direction

**Parabolic** : parabolic variation along the element local x-direction

**Cubic** : cubic variation along the element local x-direction

Calculation of section properties as per Dimensional Variation

**[Details]**

Once the main section dimensions of both ends of a tapered section member are entered, the section properties are considered to vary from the i end (element connection node N1) to the j end (element connection node N2) along the member length. The cross sectional areas, effective shear areas and torsional resistances are assumed to vary linearly from i to j along the element local x-axis. The moments of inertia are assumed to vary linearly, parabolically or cubically depending on the directions of section changes.

For instance, in the figures below, the variations of Iyy and Izz can be expressed as follows:

Moments of Inertia about strong and weak axes for a rectangular section <See figure below>

When the width (B) is constant and the height (H) varies, the moments of inertia show a cubic variation about the strong axis and a linear variation about the weak axis. Namely, Iyy Variation = 'Cubic', Izz Variation = 'Linear'.

Moments of Inertia about strong and weak axes for an I-section <See figure below>

When the width (B) is constant and the height (H) varies, the moment of inertia about the strong axis shows a nearly parabolic variation if the 1st and 2nd terms are neglected in the above equation. The moment of inertia about the weak axis varies almost linearly. Hence, it is feasible to use Iyy Variation = 'Parabolic', Izz Variation = 'Linear'. On the other hand, when the height (H) is constant and the width (B) varies, the moment of inertia about the strong axis varies almost linearly and the moment of inertia about the weak axis shows a nearly cubic variation. Hence, it is feasible to use Iyy Variation = 'Linear', Izz Variation = 'Cubic'.

**Entry of section data for a tapered section member**

In the results produced in contours, diagrams and tables, dimensional variation in the axial direction affects the moment of inertia only. In Beam Detail Analysis, section properties are directly calculated at 1/4, 1/2 and 3/4 points using the shape information. As such, dimensional variation affects all the section properties (A, Asy, Asz, Ixx, Iyy & Izz).

### Consider Warping Effect(7th DOF)

You have the option to consider the torsional effects. When there is an uneven torsion resulting from the restricted torsional displacement, torque is resisted by St. Venant's torsional shear stress and warping torsion. In cases involving curved members, eccentric loads, or differences between the center of gravity and the shear center, simulating the warping torsion effect using a 1D beam element can provide more accurate results.

When considering the warping effect (7 degrees of freedom), the warping coefficient (Iw), warping functions (w1, w2, w3, w4), and shear deformations due to the twisting moment can be checked in the sectional properties dialog box.

Applicable element types : General beam/Tapered beam

Applicable boundary condition types : Supports, Beam End Release

Applicable analysis types : Linear Static, Eigenvalue, Buckling, Response Spectrum, Construction Stage Analysis, Moving Load Analysis

Post-processing results : Reviewable in reaction forces, displacements, member forces, and stresses.