# Verification Examples

Motto:

,,There is singularity between linear and nonlinear world.”

*(Dr. Imre Bojtár)*

Verification Examples is a collection of calculation examples that compare FEM-Design analysis with hand calculations.

We are continuously developing this verification book therefore some discrepancy in the numbering of the chapters or some missing examples can occur. The Verification Manual is available as pdf book.

# 1 Linear static calculations

1.1 Beam with two point loading at one-third of its span

1.2 Calculation of a circular plate with concentrated force at its center

1.3 A simply supported square plate with uniform load

1.4 Peak smoothing of the bending moments in a flat slab

## 2 Second order analysis

2.1 A column with vertical and horizontal loads

2.2 A plate with in-plane and out-of-plane loads

## 3 Stability analysis

3.1 Flexural buckling analysis of a beam model with different boundary conditions

3.2 Buckling analysis of a plate with shell model

3.3 Lateral torsional buckling of an I section with shell model

3.4 Lateral torsional buckling of a cantilever with elongated rectangle section

## 4 Calculation of eigenfrequencies with linear dynamic theory

4.1 Continuous mass distribution on a cantilever column

4.2 Free vibration shapes of a clamped circular plate due to its self-weight

## 5 Seismic calculation

5.1 Lateral force method with linear shape distribution on a cantilever

5.2 Lateral force method with fundamental mode shape distribution on a cantilever

5.3 Modal analysis of a concrete frame building

## 6 Calculation considering diaphragms

6.1. A simple calculation with diaphragms

6.2. The calculation of the shear center

## 7 Calculations considering nonlinear effects

7.1 Uplift calculation

7.1.1 A trusses with limited compression members

7.1.2 A continuous beam with three supports

7.2 Cracked section analysis by reinforced concrete elements

7.2.1 Cracked deflection of a simply supported beam

7.2.2 Cracked deflection of a statically indeterminate beam

7.2.3 Cracked deflection of a cantilever beam

7.2.4 Cracked deflection of a cantilever beam with compressed reinforcement bars

7.2.5 Cracked deflection of a cantilever with bending moment and normal forces

7.2.6 Cracked deflection of a simply supported square slab

7.3 Nonlinear soil calculation

7.4 Elasto-plastic calculations

7.4.1 Elasto-plastic point support in a beam

7.4.2 Elasto-plastic line support in a plate

7.4.3 Elasto-plastic surface support with detach in an embedded plate

7.4.4 Elasto-plastic trusses in a multispan continuous beam

7.4.5 Elasto-plastic point-point connection between cantilevers

7.4.6 Elasto-plastic point-point connection with uplift in a multispan continuous beam

7.4.7 Elasto-plastic edge connections in a building braced by shear walls

7.4.8 Elasto-plastic edge connections with detach in a shear wall

7.4.9 Elasto-plastic line-line connections in a square plate

7.5 Calculation with construction stages

7.5.1 A steel frame building with construction stages calculation

## 8 Dynamic response analysis

8.1 Footfall analysis of a concrete footbridge

8.2 Footfall analysis of a composite floor

8.3 Footfall analysis of a lightweight floor

8.4 Footfall analysis of a small stage with rhythmic crowd load

8.5 Dynamic response of a moving mass point on a simply supported beam

8.6 Dynamic response of a moving single force on a simply supported beam

8.7 Dynamic response of a moving force group on a simply supported beam

## 9 Design calculations

#### 9.1 Foundation design

9.1.1 Design of an isolated foundation

9.1.2 Design of a wall foundation

9.1.3 Design of a foundation slab

#### 9.2 Reinforced concrete design

9.2.1 Moment capacity calculation for beams under pure bending

9.2.1.1 Under-reinforced cross section

9.2.1.2 Normal-reinforced cross section

9.2.1.3 Over-reinforced cross section

9.2.2 Required reinforcement calculation for a slab

9.2.2.1 Elliptic bending

9.2.2.2 Hyperbolic bending

9.2.3 Shear capacity calculation

9.2.3.1 Shear capacity of a beam

9.2.3.2 Shear capacity of a slab

9.2.4 Crack width calculation of a beam

9.2.5 Crack width calculation of a slab

9.2.5.1 Elliptic bending

9.2.5.2 Hyperbolic bending

9.2.6 Punching calculation of a slab

9.2.6.1 Bended bars

9.2.6.2 Circular stirrups

9.2.6.3 Open stirrups

9.2.6.4 Stud rail general product

9.2.6.5 Stud rail PSB product according to ETA-13/0151

9.2.7 Interaction of normal force and biaxial bending in a column

9.2.7.1 Nominal stiffness method

9.2.7.2 Nominal curvature method

9.2.8 Calculation of a statically indeterminate beam with post tensioned cables

#### 9.3 Steel design

9.3.1 Interaction of normal force, bending moment and shear force

9.3.2 Buckling of a doubly symmetric I section

9.3.3 Buckling of a doubly symmetric + section

9.3.4 Buckling of a mono-symmetric channel section

9.3.5 Lateral torsional buckling of a doubly symmetric I section

9.3.6 Interaction of biaxial bending and axial compression in an RHS section

9.3.7 Interaction calculation with a Class 4 section

#### 9.4 Timber design

9.4.1 Design of timber bars

9.4.2 CLT Panel design with laminated composite shell theory

9.4.2.1 Calculation with shear coupling

9.4.2.1.1.1 Glue at narrow side

9.4.2.1.1.2 No glue at narrow side

9.4.2.1.2 Calculation without shear coupling

9.4.2.1.2.1 Glue at narrow side

9.4.2.1.2.2 No glue at narrow side

9.4.2.2 Deflection and stresses of a CLT panel supported on two opposite edges

9.4.2.3 Deflection and stresses of a CLT simply supported two-way slab

9.4.2.4 In-plane loaded CLT design check to shear failure at glued contact surface

9.4.2.5 Buckling check of a CLT wall

#### 9.5 Automatic calculation of flexural buckling length

9.5.1 Concrete frame building

9.5.1.1 Non-sway case

9.5.1.2 Sway case

9.5.2 Steel frame building

9.5.2.1 Non-sway case

9.5.2.2 Sway case

9.5.3 A column and a supporting beam with various angles

## 10 Cross section editor

10.1 Calculation of a compound cross section

References

Notes