4784x

002715

2024-01-16

Select Manual

Overview

Graphical User Interface and Settings

Load Cases and Combinations

Stresses

In the navigator, define the stresses to be displayed on the surfaces. The table lists the stresses of each surface according to the specifications set in the Result Table Manager .

01 Selecting Surface Stresses in Navigator

02 Surface Stresses in Table

The surface stresses are subdivided into the following categories:

Basic Stresses: stresses in the direction of the surface axes
Principal Stresses: stresses in the direction of the principal axes
Elastic Stress Components: stresses from moments and axial forces
Equivalent Stresses: stresses according to various equivalent stress hypotheses

Basic stresses

Basic stresses are related to the directions of the local surface axes. When analyzing curved surfaces, they refer to the local axes of finite elements (see image Displaying FE Axis Systems ).

The basic stresses are shown in the Surface Internal Forces and Surface Stresses image. They have the following meanings:

σ_{x, +} = \frac{n_{x}}{d} + \frac{6 m_{x}}{d^{2}}

d	thickness of surface

Stress σ_x,+ (in Direction of Local x-Axis on Positive Surface Side)

σ_{y, +} = \frac{n_{y}}{d} + \frac{6 m_{y}}{d^{2}}

Stress σ_y,+ (in Direction of Local y-Axis on Positive Surface Side)

σ_{x, -} = \frac{n_{x}}{d} - \frac{6 m_{x}}{d^{2}}

Stress σ_x,- (in Direction of x-Axis on Negative Surface Side)

σ_{y, -} = \frac{n_{y}}{d} - \frac{6 m_{y}}{d^{2}}

Stress σ_y,- (in Direction of y-Axis on Negative Surface Side)

τ_{x y, +} = \frac{n_{x y}}{d} + \frac{6 m_{x y}}{d^{2}}

Torsional Stress τ_xy,+ on Positive Surface Side

τ_{x y, -} = \frac{n_{x y}}{d} - \frac{6 m_{x y}}{d^{2}}

Torsional Stress τ_xy,- on Negative Surface Side

τ_{x z} = \frac{3 v_{x}}{2 d}

Shear Stress τ_xz Perpendicular to Surface in Direction of x-Axis

τ_{y z} = \frac{3 v_{y}}{2 d}

Shear Stress τ_yz Perpendicular to Durface in Direction of y-Axis

Principal stresses

While the basic stresses refer to the xyz coordinate system of a surface, the principal stresses represent the extreme values of the stresses in a surface element. The principal axes 1 (maximum value) and 2 (minimum value) are arranged orthogonally. It is possible to graphically display the principal axis directions α as Trajectories (compare image Displaying Trajectories of Principal Axes ).

The principal stresses are determined from the basic stresses as follows:

σ_{1, +} = \frac{1}{2} [σ_{x, +} + σ_{y, +} + \sqrt{{(σ_{x, +} - σ_{y, +})}^{2} + 4 {τ_{x y, +}}^{2}}]

Stress σ_1,+ in Direction of Principal Axis 1 on Positive Surface Side

σ_{2, +} = \frac{1}{2} [σ_{x, +} + σ_{y, +} - \sqrt{{(σ_{x, +} - σ_{y, +})}^{2} + 4 {τ_{x y, +}}^{2}}]

Stress σ_2,+ in Direction of Principal Axis 2 on Positive Surface Side

α_{+} = \frac{1}{2} \arctan 2 (\frac{2 τ_{x y, +}}{σ_{x, +} - σ_{y, +}}) \in (- 90 °, 90 °]

Angle α₊ Between Local Axis x (or y) and Principal Axis 1 (or 2) for Stresses on Positive Surface Side

σ_{1, -} = \frac{1}{2} [σ_{x, -} + σ_{y, -} + \sqrt{{(σ_{x, -} - σ_{y, -})}^{2} + 4 {τ_{x y, -}}^{2}}]

Stress σ_1,- in Direction of Principal Axis 1 on Negative Surface Side

σ_{2, -} = \frac{1}{2} [σ_{x, -} + σ_{y, -} - \sqrt{{(σ_{x, -} - σ_{y, -})}^{2} + 4 {τ_{x y, -}}^{2}}]

Stress σ_2,- in Direction of Principal Axis 2 on Negative Surface Side

α_{-} = \frac{1}{2} \arctan 2 (\frac{2 τ_{x y, -}}{σ_{x, -} - σ_{y, -}}) \in (- 90 °, 90 °]

Angle α_- Between Local Axis x (or y) and Principal Axis 1 (or 2) for Stresses on Negative Surface Side

σ_{1, m} = \frac{1}{2} [σ_{x, m} + σ_{y, m} + \sqrt{{(σ_{x, m} - σ_{y, m})}^{2} + 4 {τ_{x y, m}}^{2}}]

Membrane Stress σ_1,m in Direction of Principal Axis 1

σ_{2, m} = \frac{1}{2} [σ_{x, m} + σ_{y, m} - \sqrt{{(σ_{x, m} - σ_{y, m})}^{2} + 4 {τ_{x y, m}}^{2}}]

Membrane Stress σ_2,m in Direction of Principal Axis 2

α_{m} = \frac{1}{2} \arctan 2 (\frac{2 τ_{x y, m}}{σ_{x, m} - σ_{y, m}}) \in (- 90 °, 90 °]

Angle α_m Between Local Axis x and Principal Axis 1 for Membrane Stresses

τ_{\max} = \sqrt{{τ_{x z}}^{2} + {τ_{y z}}^{2}}

Maximum Shear Stress τ_max Perpendicular to Surface

Other stresses/Elastic stress components

This category includes stress components due to bending moments and membrane forces. They are related to the directions of the local surface axes. When curved surfaces are analyzed, they refer to the axes of the finite elements.

The bending and membrane stresses have the following meanings:

σ_{x, b} = \frac{6 m_{x}}{d^{2}}

d	Thickness of the surface

Stress σ_x,b Due to Bending Moment m_x

σ_{y, b} = \frac{6 m_{y}}{d^{2}}

Stress σ_y,b Due to Bending Moment m_y

τ_{x y, b} = \frac{6 m_{x y}}{d^{2}}

Stress τ_xy,b Due to Torsional Moment m_xy

σ_{x, m} = \frac{n_{x}}{d}

Membrane Stress σ_x,m Due to Axial Force n_x

σ_{y, m} = \frac{n_{y}}{d}

Membrane Stress σ_y,m Due to Axial Force n_y

τ_{x y, m} = \frac{n_{x y}}{d}

Stress τ_{xy, m} Due to Shear Flow n_xy

Equivalent stresses

The Basic Stresses are combined according to four equivalent stress hypotheses for the plane stress state.

von Mises

The approach by von Mises is also called "shape modification hypothesis". It is based on the assumption that the material fails when the distortion strain energy exceeds a certain limit. This energy is the type of energy that causes a distortion or deformation of the object. This approach represents the most well-known and most frequently used equivalent stress hypothesis. It is suitable for all materials that are not brittle. Therefore, it is widely used in steel building construction. The von Mises hypothesis is not suitable for hydrostatic stress conditions with equal principal stresses in all directions, as the equivalent stress is zero in such a case.

The equivalent stresses according to von Mises for the plane state of stress have the following meanings:

σ_{v, Mises, Max} = \max (σ_{v, Mises, +}; σ_{v, Mises, -})

Maximum Equivalent Stress σ_v,Mises,max on Positive or Negative Surface Side

σ_{v, Mises, +} = \sqrt{{σ_{x, +}}^{2} + {σ_{y, +}}^{2} - σ_{x, +} σ_{y, +} + 3 {τ_{x y, +}}^{2}}

Equivalent Stress σ_v,Mises,+ on Positive Surface Side

σ_{v, Mises, -} = \sqrt{{σ_{x, -}}^{2} + {σ_{y, -}}^{2} - σ_{x, -} σ_{y, -} + 3 {τ_{x y, -}}^{2}}

Equivalent Stress σ_v,Mises,- on Negative Surface Side

σ_{v, Mises, m} = \sqrt{{σ_{x, m}}^{2} + {σ_{y, m}}^{2} - σ_{x, m} σ_{y, m} + 3 {τ_{x y, m}}^{2}}

Membrane Equivalent Stress σ_v,Mises,m

Tresca

The approach by Tresca is also known as the "maximum shear stress theory". It is assumed that failure is caused by the maximum shear stress. As this hypothesis is especially applicable for brittle materials, it is frequently used in mechanical engineering.

The equivalent stresses according to Tresca are determined as follows:

σ_{v, Tresca, Max} = \max (σ_{v, Tresca, +}; σ_{v, Tresca, -})

Maximum Equivalent Stress σ_v,Tresca,max on Positive or Negative Surface Side

σ_{v, Tresca, +} = \max (|σ_{1, +} - σ_{2, +}|; |σ_{2, +}|; |σ_{1, +}|) or

σ_{v, Tresca, +} = \max (\sqrt{{(σ_{x, +} - σ_{y, +})}^{2} + 4 {τ_{xy, +}}^{2}}; |σ_{2, +}|; |σ_{1, +}|)

Equivalent Stress σ_v,Tresca,+ on Positive Surface Side

σ_{v, Tresca, -} = \max (|σ_{1, -} - σ_{2, -}|; |σ_{2, -}|; |σ_{1, -}|) or

σ_{v, Tresca, -} = \max (\sqrt{{(σ_{x, -} - σ_{y, -})}^{2} + 4 {τ_{xy, -}}^{2}}; |σ_{2, -}|; |σ_{1, -}|)

Equivalent Stress σ_v,Tresca,- on Negative Surface Side

σ_{v, Tresca, m} = \max (|σ_{1, m} - σ_{2, m}|; |σ_{2, m}|; |σ_{1, m}|) or

σ_{v, Tresca, m} = \max (\sqrt{{(σ_{x, m} - σ_{y, m})}^{2} + 4 {τ_{xy, m}}^{2}}; |σ_{2, m}|; |σ_{1, m}|)

Membrane Equivalent Stress σ_v,Tresca,m

Rankine

The equivalent stress hypothesis by Rankine is also known as the "maximum principal stress criterion". It is assumed that the maximum principal stress leads to failure.

The equivalent stresses according to Rankine are determined as follows:

σ_{v, Rankine, Max} = \max (σ_{v, Rankine, +}; σ_{v, Rankine, -})

Maximum Equivalent Stress σ_{v,Rankine,max} on Positive or Negative Surface Side

σ_{v, Rankine, +} = \frac{1}{2} |σ_{x, +} + σ_{y, +}| + \frac{1}{2} \sqrt{{(σ_{x, +} - σ_{y, +})}^{2} + 4 {τ_{xy, +}}^{2}}

Equivalent Stress σ_v,Rankine,+ on Positive Surface Side

σ_{v, Rankine, -} = \frac{1}{2} |σ_{x, -} + σ_{y, -}| + \frac{1}{2} \sqrt{{(σ_{x, -} - σ_{y, -})}^{2} + 4 {τ_{xy, -}}^{2}}

Equivalent Stress σ_v,Rankine,- on Negative Side of Surface

σ_{v, Rankine, m} = \frac{1}{2} |σ_{x, m} + σ_{y, m}| + \frac{1}{2} \sqrt{{(σ_{x, m} - σ_{y, m})}^{2} + 4 {τ_{xy, m}}^{2}}

Equivalent Stress σ_{v, Rankine,m}

Bach

The equivalent stress hypothesis according to Bach is also referred to as the "principal strain hypothesis". It is assumed that failure occurs in the direction of the greatest strain. This statement is similar to the stress analysis according to Rankine. However, the principal strain is used instead of the principal stress in this case.

The equivalent stresses according to Bach are determined as follows:

σ_{v, Bach, Max} = \max (σ_{v, Bach, +}; σ_{v, Bach, -})

Maximum Equivalent Stress σ_v,Bach,max on Positive or Negative Surface Side

σ_{v, Bach, +} = \max (\frac{1 - ν}{2} |σ_{x, +} + σ_{y, +}| + \frac{1 + ν}{2} \sqrt{{(σ_{x, +} - σ_{y, +})}^{2} + 4 {τ_{xy, +}}^{2}}; ν |σ_{x, +} + σ_{y, +}|)

ν	Poisson's ratio

Equivalent Stress σ_v,Bach,+ on Positive Surface Side

σ_{v, Bach, -} = \max (\frac{1 - ν}{2} |σ_{x, -} + σ_{y, -}| + \frac{1 + ν}{2} \sqrt{{(σ_{x, -} - σ_{y, -})}^{2} + 4 {τ_{xy, -}}^{2}}; ν |σ_{x, -} + σ_{y, -}|)

Equivalent Stress σ_v,Bach,- on Negative Surface Side

σ_{v, Bach, m} = \max (\frac{1 - ν}{2} |σ_{x, m} + σ_{y, m}| + \frac{1 + ν}{2} \sqrt{{(σ_{x, m} - σ_{y, m})}^{2} + 4 {τ_{xy, m}}^{2}}; ν |σ_{x, m} + σ_{y, m}|)

Membrane Equivalent Stress σ_v,Bach,m

Parent section

Results by Surface

Events

2024-04-24

Online Training

RFEM 6 | Students | Introduction to FEM

2024-04-30

Online Training

RFEM 6 | Students | Introduction to Timber Design

2024-05-08

Online Training

RFEM 6 | Students | Introduction to Reinforced Concrete Design

2024-05-15

Online Training

RFEM 6 | Students | Introduction to Steel Design

2024-05-23

Most Frequently Asked Questions Answered by Dlubal Support Team

Webinar

Most Frequently Asked Questions Answered by Dlubal Support Team | May 2024

2024-06-20

Webinar

Most Frequently Asked Questions Answered by Dlubal Support Team | June 2024

2024-10-16

Online Training

RFEM 6 | Students | Introduction to Member Design

2024-10-23

Online Training

RSECTION 1 | Students | Introduction to Strength of Materials

2024-10-30

Online Training

RFEM 6 | Students | Introduction to FEM

2024-11-06

Online Training

RFEM 6 | Students | Introduction to Steel Design

2024-11-13

Online Training

RFEM 6 | Students | Introduction to Reinforced Concrete Design

2024-11-20

Online Training

RFEM 6 | Students | Introduction to Timber Design

Videos

FAQ

[EN] FAQ 004348 | After dividing a column with intermediate nodes, the results in the RF‑/CONCRETE ...

Length: 00:00:59 min

FAQ

[EN] FAQ 004270 | Is it possible to use high-strength reinforcement or high-strength reinforcing steel in the ...

Length: 00:00:56 min

FAQ

[EN] FAQ 000466 | I want to rotate a graphic in my printout report by 90 degrees. What is ...

Length: 00:00:34 min

Product Feature

Punching Shear Design for All Section Shapes

Length: 00:00:00 min

FAQ

FAQ 005472 | In the table of the objects to be designed in the Concrete Design add-on, punching nodes are...

Length: 00:00:00 min

Product Feature

Automatic to Reach Specific Effective Modal Mass Factor

Length: 00:00:55 min

Product Feature

Info Bubbles for Line Supports

Length: 00:00:35 min

Event

Calculation of Reinforced Concrete Slabs in RFEM 6

Length: 01:09:36 min

Event

Webinar | Geotechnical Analysis in RFEM 6

Length: 01:04:37 min

Playlist

Models to Download

171x

Pedestrian and Cyclist Bridge in Eichstätt, Germany

174x

20x

Concrete Bridge

215x

17x

Concrete Building

313x

62x

Angled Office Building

339x

26x

Twin Pile Cap

295x

22x

Triple Pile Cap

353x

25x

Foundation Footing

Model 004786 | Office Building with Integrated Visitors' Center and Parking Garage in Geiselbulach, Germany

326x

Office Building with Integrated Visitor Center and Parking Garage in Geiselbulach, Germany

269x

12x

Bleachers

Knowledge Base Articles

When calculating the internal forces for the buckling analysis with the method based on nominal curvature in RF‑CONCRETE Columns, the required eccentricities have to be determined.

Determining Degree of Restraint of Column Ends Taking into Account Stiffness of Connected Beams

Effective lengths for columns can be determined automatically with RF-/CONCRETE Columns. This article describes which entries are necessary and how the calculation of the effective lengths is performed.

The fatigue design according to EN 1992-1-1 must be performed for the structural components subjected to large stress ranges and/or many load changes. In this case, the design checks for the concrete and the reinforcement are performed separately. There are two alternative design methods available.

Using an example of a steel fiber-reinforced concrete slab, this article describes how the use of different integration methods and of a different number of integration points affects the calculation result.

Product Features

Feature 002801 | Punching Shear Design for All Section Shapes

Do you have individual column sections and angled wall geometries, and need punching shear design for them?

No problem. In RFEM 6, you can perform punching shear design not only for rectangular and circular sections, but for any cross-section shape.

Feature 002722 | Sensitivity Coefficient

For a response spectrum analysis of building models, you can display the sensitivity coefficients for the horizontal directions by story.

These key figures allow you to interpret the sensitivity to stability effects.

Feature 002720 | Modal Relevance Factor for Stability Analysis

The modal relevance factor (MRF) can help you to assess to which extent specific elements participate in a specific mode shape. The calculation is based on the relative elastic deformation energy of each individual member.

The MRF can be used to distinguish between local and global mode shapes. If multiple individual members show significant MRF (for example, > 20%), the instability of the entire structure or a substructure is very likely. On the other hand, if the sum of all MRFs for an eigenmode is around 100%, a local stability phenomenon (for example, buckling of a single bar) can be expected.

Furthermore, the MRF can be used to determine critical loads and equivalent buckling lengths of certain members (for example, for stability design). Mode shapes for which a specific member has small MRF values (for example, < 20%) can be neglected in this context.

The MRF is displayed by mode shape in the result table under Stability Analysis → Results by Members → Effective Lengths and Critical Loads.

You can use the "Plate Cut" component to cut plates (for example, gusset plates, fin plates, and so on). There are various cutting methods available:

Plane: The cut is performed on the closest surface to the reference plate.
Surface: Only the intersecting parts of plates are cut.
Bounding Box: The outermost dimension consisting of width and height is cut out of the plate as a rectangle.
Convex Envelope: The outer hull of the cross-section is used for the plate cut. If there are fillets at the corner nodes of the cross-section, the cut is adapted to them.