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    7
1.2 Calculation of a circular plate with concentrated force at its center    9
1.3 A simply supported square plate with uniform load    13
1.4 Peak smoothing of the bending moments in a flat slab    16

2 Second order analysis

2.1 A column with vertical and horizontal loads    21
2.2 A plate with in-plane and out-of-plane loads    24

3 Stability analysis

3.1 Flexural buckling analysis of a beam model with different boundary conditions    28
3.2 Buckling analysis of a plate with shell model    31
3.3 Lateral torsional buckling of an I section with shell model    34
3.4 Lateral torsional buckling of a cantilever with elongated rectangle section    37

4 Calculation of eigenfrequencies with linear dynamic theory

4.1 Continuous mass distribution on a cantilever column    39
4.2 Free vibration shapes of a clamped circular plate due to its self-weight    42

5 Seismic calculation

5.1 Lateral force method with linear shape distribution on a cantilever    44
5.2 Lateral force method with fundamental mode shape distribution on a cantilever    47
5.3 Modal analysis of a concrete frame building    49
6 Calculation considering diaphragms    58
6.1. A simple calculation with diaphragms    58
6.2. The calculation of the shear center    58
7 Calculations considering nonlinear effects    63
7.1 Uplift calculation    63
7.1.1 A trusses with limited compression members    63
7.1.2 A continuous beam with three supports     67
7.2 Cracked section analysis by reinforced concrete elements    73
7.2.1 Cracked deflection of a simly supported beam    73
7.2.2 Cracked deflection of a statically indeterminate beam    79
7.2.3 Cracked deflection of a cantilever beam    85
7.2.4 Cracked deflection of a cantilever beam with compressed reinforcement bars    90
7.2.5 Cracked deflection of a cantilever with bending moment and normal forces    94
7.2.6 Cracked deflection of a simply supported square slab    103
7.3 Nonlinear soil calculation    110
7.4 Elasto-plastic calculations    111
7.4.1 Elasto-plastic point support in a beam    111
7.4.2 Elasto-plastic line support in a plate    116
7.4.3 Elasto-plastic surface support with detach in an embedded plate    121
7.4.4 Elasto-plastic trusses in a multispan continuous beam    131
7.4.5 Elasto-plastic point-point connection between cantilevers    141
7.4.6 Elasto-plastic point-point connection with uplift in a multispan continuous beam    145
7.4.7 Elasto-plastic edge connections in a building braced by shear walls    151
7.4.8 Elasto-plastic edge connections with detach in a shear wall    155
7.4.9 Elasto-plastic line-line connections in a square plate    161
7.5 Calculation with construction stages    165
7.5.1 A steel frame building with construction stages calculation    165
8 Footfall analysis    171
8.1 Footfall analysis of a concrete footbridge    171
8.2 Footfall analysis of a composite floor    175
8.3 Footfall analysis of a lightweight floor    177
8.4 Footfall analysis of a small stage with rhythmic crowd load    179
9 Design calculations    183
9.1 Foundation design    183
9.1.1 Design of an isolated foundation    183
9.1.2 Design of a wall foundation    183
9.1.3 Design of a foundation slab     183
9.2 Reinforced concrete design    184
9.2.1 Moment capacity calculation for beams under pure bending    184
9.2.1.1 Under-reinforced cross section    184
9.2.1.2 Normal-reinforced cross section    191
9.2.1.3 Over-reinforced cross section    194
9.2.2 Required reinforcement calculation for a slab    197
9.2.2.1 Elliptic bending    197
9.2.2.2 Hyperbolic bending    207
9.2.3 Shear capacity calculation    217
9.2.3.1 Shear capacity of a beam    217
9.2.3.2 Shear capacity of a slab    220
9.2.4 Crack width calculation of a beam    224
9.2.5 Crack width calculation of a slab    230
9.2.5.1 Elliptic bending    231
9.2.5.2 Hyperbolic bending    243
9.2.6 Punching calculation of a slab    265
9.2.6.1 Bended bars    266
9.2.6.2 Circular stirrups    271
9.2.6.3 Open stirrups    274
9.2.6.4 Stud rail general product    277
9.2.6.5 Stud rail PSB product according to ETA-13/0151    280
9.2.7 Interaction of normal force and biaxial bending in a column    284
9.2.7.1 Nominal stiffness method    285
9.2.7.2 Nominal curvature method    292
9.2.8 Calculation of a statically indeterminate beam with post tensioned cables    296
9.3 Steel design    305
9.3.1 Interaction of normal force, bending moment and shear force    305
9.3.2 Buckling of a doubly symmetric I section    310
9.3.3 Buckling of a doubly symmetric + section    315
9.3.4 Buckling of a mono-symmetric channel section    320
9.3.5 Lateral torsional buckling of a doubly symmetric I section    327
9.3.6 Interaction of biaxial bending and axial compression in an RHS section    332
9.3.7 Interaction calculation with a Class 4 section    343
9.4 Timber design    344
9.5 Automatic calculation of flexural buckling length    345
9.5.1 Concrete frame building    345
9.5.1.1 Non-sway case    345
9.5.1.2 Sway case    348
9.5.2 Steel frame building    350
9.5.2.1 Non-sway case    350
9.5.2.2 Sway case    352
9.5.3 A column and a supporting beam with various angles    355
10 Cross section editor    358
10.1 Calculation of a compound cross section    358
References    360
Notes     361