Bar structures – BuildSoft Support https://support.buildsoft.eu BuildSoft Support Mon, 12 Jan 2026 09:00:58 +0000 en-US hourly 1 https://wordpress.org/?v=6.2.14 DLL 06: Cantilever beam with eccentric mass – eigenfrequencies https://support.buildsoft.eu/knowledge-base/cantilever-beam-with-eccentric-mass-eigenfrequencies/ Fri, 08 Dec 2023 16:36:00 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=11576 Description

Material For bar AB Modulus of elasticity E=210 000 N/mm^2
Density \rho=7800 kg/m^3
 For bar BC1 Modulus of elasticity E=999 999 N/mm^2
Density \rho=0.010 kg/m^3
Geometry Cross-section For all bars d_e = 0.35m
d_i = 0.32 m
Boundary conditions In point A Fixed support
Loads Case 1: Mass of 1000 kg in point B.
Bar BC is not present.
Case 2: Mass of 1000 kg in point C.
Bar BC is present.
Mesh No. of divisions 12

1. The eccentricity of the mass is created by adding bar BC to the model. The purpose is that bar BC is significantly stiffer than bar AB.

Results

Case 1

Eigen mode Shape Independent reference Diamonds Difference
1 1.65Hz 1.655Hz -0.30%
2 16.07Hz 16.07Hz 0.00%
3 50.02Hz 50.027Hz -0.01%
4 76.47Hz 76.45Hz 0.03%
5 80.47Hz 80.505Hz -0.04%
6 103.2Hz 103.235Hz -0.03%

Case 2

Eigen mode Shape Independent reference Diamonds Difference
1 1.636Hz 1.635Hz 0.06%
2 1.642Hz 1.641Hz 0.06%
3 13.46Hz 13.391Hz 0.52%
4 13.59Hz 13.562Hz 0.21%
5 28.9Hz 28.821Hz 0.27%
6 31.96Hz 30.872Hz 3.52%
7 61.61Hz 61.618Hz -0.01%
8 63.93Hz 61.969Hz 3.16%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 15: poutre encastrée-libre avec masse ou inertie excentrée
  • Tested in Diamonds 2026.
]]> TLL 01: Beam under temperature load https://support.buildsoft.eu/knowledge-base/tll-01-beam-under-temperature-load/ Thu, 30 Nov 2023 14:06:20 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=11125 Description

Material Modulus of elasticity E=210 000 N/mm^2
Thermal dilation \alpha =0.000 012/ ^{\circ}C
Geometry Cross-section IPE 500
Boundary conditions Case 1: cantilever
Case 2: fixed beam
Loads Load 1: Global temperature change \Delta T = 40 ^{\circ}C
Load 2: Linear gradient in local y’ direction \Delta T = 40 ^{\circ}C
Load 3: Linear gradient in local z’ direction \Delta T = 40 ^{\circ}C
Mesh No. of divisions 8

Independent reference results

Open handcalculations

Load 1: global temperature change \Delta T = 40 ^{\circ}C

  • Case 1: cantilever beam
    Since the beam can lengthen/ shorten, the temperature load will extend the beam

    \[ \delta_x=\alpha \cdot \Delta T\cdot L=0.000 012 / ^{\circ}C\cdot 40^{\circ}C\cdot 5m=2.4mm\]

  • Case 2: fixed beam
    Since the beam cannot lengthen/ shorten, the temperature load will result in axial force.
    The increase in temperature will want to lengthen the beam. To counteract this deformation, a compressive force must be created. So the normal force in Diamonds will have a negative sign.

    \[N=\alpha \cdot \Delta T\cdot A\cdot E=0.000 012 / ^{\circ}C\cdot 40^{\circ}C\cdot 11553mm^2\cdot 210000N/mm^2=1164.46kN\]

Load 2: linear gradient in local y’ direction \Delta T = 40 ^{\circ}C

  • Case 1: cantilever beam
    Since the beam can lengthen/ shorten, the gradient will cause an elongation of the upper fiber and a shortening of the non-fiber. The combination of both results in a downward deformation.

        \[ \varphi_z=\frac{\alpha \cdot \Delta T\cdot L}{h}=\frac{0.000 012 / ^{\circ}C\cdot 40^{\circ}C\cdot 11553mm^2\cdot 5m}{500mm}=0.2750^{\circ}\]

        \[ \delta _y=\frac{\alpha \cdot \Delta T\cdot L^2}{2 \cdot h}=\frac{0.000 012 / ^{\circ}C\cdot 40^{\circ}C\cdot (5m)^2}{2 \cdot 500mm}=12.0000mm\]

  • Case 2: Fixed beam
    Since the beam cannot lengthen/ shorten, the gradient will cause an elongation of the upper fiber and a shortening of the non-fiber. To counteract this deformation, a compressive force must be created in the upper fiber and a tensile force in the lower. So the bending moment in Diamonds will be drawn on the lower side of the beam.

        \[M_{y'}=\frac{\alpha \cdot \Delta T\cdot E\cdot I_y}{h}=\frac{0.000 012 / ^{\circ}C\cdot 40^{\circ}C \cdot 4.82\cdot 10^8 mm^4}{500mm}=97.17kNm\]

Load 3: linear gradient in local z’ direction \Delta T = 40 ^{\circ}C

  • Case 1: cantilever beam
    Since the beam can lengthen/ shorten, the gradient will cause an elongation of the upper fiber and a shortening of the non-fiber. The combination of both results in a downward deformation.

        \[ \varphi_z=\frac{\alpha \cdot \Delta T\cdot L}{b}=\frac{0.000 012 / ^{\circ}C\cdot 40^{\circ}C\cdot 11553mm^2\cdot 5m}{200mm}=0.6875^{\circ}\]

        \[ \delta _y=\frac{\alpha \cdot \Delta T\cdot L^2}{2 \cdot b}=\frac{0.000 012 / ^{\circ}C\cdot 40^{\circ}C\cdot (5m)^2}{2 \cdot 200mm}=30.0000mm\]

  • Case 2: Fixed beam
    Since the beam cannot lengthen/ shorten, the gradient will cause an elongation of the upper fiber and a shortening of the non-fiber. To counteract this deformation, a compressive force must be created in the upper fiber and a tensile force in the lower. So the bending moment in Diamonds will be drawn on the lower side of the beam.

        \[M_{y'}=\frac{\alpha \cdot \Delta T\cdot E\cdot I_y}{b}=\frac{0.000 012 / ^{\circ}C\cdot 40^{\circ}C \cdot 2.14\cdot 10^7 mm^4}{200mm}=10.79kNm\]

Diamonds results and comparison

Load 1: global temperature change \Delta T = 40 ^{\circ}C


Independent reference Diamonds Difference
Case 1 Horizontal deformation \delta_x 2.4mm 2.4mm 0,00%
Case 2 Axial force N -1164.46kN -1164.46kN 0,00%

Load 2: linear gradient in local y’ direction \Delta T = 40 ^{\circ}C

Independent reference Diamonds Difference
Case 1 Angular rotation \varphi_z 0.2750° 0.2750° 0,00%
Horizontal deformation \delta_y 12.0000mm 12.0000mm 0,00%
Case 2 Bending moment M_y 97,17kNm 97,17kNm 0,00%

Load 3: linear gradient in local z’ direction \Delta T = 40 ^{\circ}C

Independent reference Diamonds Difference
Case 1 Angular rotation \varphi_y 0.6875° 0.6875° 0,00%
Horizontal deformation \delta_z 30.0000mm 30.0000mm 0,00%
Case 2 Bending moment M_z 10.79kNm 10.79kNm 0,00%

References

  • Hibbeler, R. (2006). Sterkteleer, 2/e. Pearson Education.
  • Weaver, W., & Gere, J. M. (1990). Matrix analysis of framed structures Table B-2. In Springer eBooks.
  • Tested in Diamonds 2026.
]]> DLL 02: Slender folded beam, one end fixed other free – eigenfrequencies https://support.buildsoft.eu/knowledge-base/slender-folded-beam-one-end-fixed-other-free-eigenfrequencies/ Fri, 24 Nov 2023 21:29:06 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=11081 Description

Material Modulus of elasticity E=210 000 N/mm^2
Density \rho=7800 kg/m^3
Poisson’s ratio \nu= 0.3
Geometry Cross-section Dimensions b = 50 mm
h = 5 mm
Boundary conditions In point A Fixed support
Mesh No. of divisions 12

Results

Handcalculation

    \[f_i=(2\cdot \begin{bmatrix}1 \\2 \\ 3 \\ 4 \end{bmatrix} -1 )^2\cdot \pi \cdot \frac{h}{8\cdot l^2}\cdot \sqrt{\frac{E}{12\cdot \rho }}=\begin{bmatrix}11.764 \\105.878 \\294.104 \\576.446 \end{bmatrix}Hz\]

Eigen mode Shape Independent reference Diamonds Difference
1 11,764Hz 11,757Hz 0,06%
2 105,878Hz 105.803Hz 0,07%
3 294,104Hz 293.930Hz 0,06%
4 576,445Hz 576.267Hz 0,03%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 02: poutre élancée encastrée-libre, replieée sur elle-même.
  • Tested in Diamonds 2026.
]]> DLX 05: Thin circle – fixed on elastic plate – eigenfrequencies https://support.buildsoft.eu/knowledge-base/thin-circle-fixed-on-elastic-plate-eigen-frequencies/ Thu, 16 Nov 2023 09:11:55 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=10925

Description


Material   Modulus of elasticity E=72 000 N/mm^2
  Density \rho=2700 kg/m^3
Geometry Cross-section For the circle b = 10 mm and h = 5 mm
  For the connecting plate b = 10 mm and h = 3 mm
Boundary conditions In point A Fixed support
  Along the entire edge R_z, M_x and M_y fixed to impose 2D behaviour
Mesh   No. of divisions 8

Results

Eigen mode Shape Independent reference Diamonds Difference
1 28.8Hz 28.9Hz -0.35%
2 189.3Hz 190.0Hz -0.37%
3 286.8Hz 270.0Hz 6.22%
4 641.0Hz 643.6Hz -0.4%
5 682.0Hz 684.2Hz -0.32%
6 1063.0Hz 1065.5Hz -0.23%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 13: anneau circulaire mince suspendu par une patte élastique
  • Tested in Diamonds 2026.

]]> DLX 04: Thin circle – fixed at two points – eigen frequencies https://support.buildsoft.eu/knowledge-base/thin-circle-fixed-at-two-points-eigen-frequencies/ Wed, 15 Nov 2023 10:24:30 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=10875

Description


Material Modulus of elasticity E=7 200 000 N/mm^2
Density \rho=2700 kg/m^3
Geometry Cross-section b = 10 mm
h = 5 mm
Boundary conditions In points A at angle \alpha=120 ^{\circ} Fixed support
Along the entire edge R_z, M_x and M_y fixed to impose 2D behaviour
Mesh No. of divisions 8

Results

Handcalculation

    \[f_i=\frac{1}{2\cdot \pi}\cdot \lambda_i\cdot \frac{h}{R^2}\cdot \sqrt{\frac{E}{12\cdot \rho }}\]

    \[ f_i=\frac{1}{2\cdot \pi}\cdot \begin{bmatrix}1.9832 \\ 4.8497 \\ 9.3204 \\ 11.8490 \\ 14.7614 \\ 21.5545 \\ 23.6157 \end{bmatrix}\cdot \frac{h}{R^2}\cdot \sqrt{\frac{E}{12\cdot \rho }}= \begin{bmatrix}23.5 \\ 57.5 \\ 110.6 \\ 140.6 \\ 175.1 \\ 255.7 \\ 280.1 \end{bmatrix}Hz\]


Eigen mode Shape Independent reference Diamonds Difference
1 23.5Hz 23.6Hz -0.31%
2 57.5Hz 57.8Hz -0.47%
3 110.6Hz 111.1Hz -0.48%
4 140.6Hz 141.2Hz -0.45%
5 175.1Hz 175.9Hz -0.45%
6 255.7Hz 256.8Hz -0.43%
7 280.1Hz 281.6Hz -0.52%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 12: anneau circulaire mince encastré en deux points
    The dimensions of the Afnor example were too small for Diamonds. So the radius R and young’s modulus E have been adjusted, and the results are recalculated accordingly.

  • Tested in Diamonds 2026.

]]> DLL 04: Slender beam simply supported subjected to axial load – eigen modes – global buckling https://support.buildsoft.eu/knowledge-base/dll-04/ Sat, 04 Nov 2023 09:24:08 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=10469

Description

Material Modulus of elasticity E=200 000 N/mm^2
Density \rho=7800 kg/m^3
Poisson’s ratio \nu= 0.3
Geometry Cross-section Dimensions b=h=50mm
Boundary conditions In point A Simple support
In point B Roller support
Along line AB R_z, M_x and M_y fixed to impose 2D behaviour
Loads In point B F=10kN
Mesh No. of divisions 20

Results

Eigen modes

Eigen mode Shape Independent reference Diamonds Difference
1   28,702Hz 28,702Hz 0,00%
2   114,807Hz 114,807Hz 0,00%

Note: only the mass of vertical loads contributes to the eigenmodes. So these eigen modes are calculated with the mass of the self-weight. The horizontal force of 10kN does not contribute.

Global buckling factor

When you do a second order calculation, Diamonds calculates the global buckling factor. This global buckling factor is the factor with which the loads on the structure must be multiplied to obtain buckling. Resulting in the critial buckling force.

Equilibrium check  in Diamonds

Which result Independent reference Diamonds Difference
Critical load 257,02kN 25.702 \cdot 10 \text{kN}=257.02\text{kN} 0,00%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 05: poutre élancée sur 2 appuis, soumise à un chargement axial

  • Tested in Diamonds 2026.

]]> DLL 03: slender beam fixed at both ends with different inertia – dynamic response https://support.buildsoft.eu/knowledge-base/validation-slender-beam-fixed-at-both-ends-with-different-inertia-dynamic-response/ Fri, 03 Nov 2023 17:22:20 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=10435

Description

Material Modulus of elasticity E=210 000 N/mm^2
Density \rho=7850 kg/m^3
Poisson’s ratio \nu= 0.3
Geometry Cross-section For bars AB IPE 200
For bar BB IPE 300
Boundary conditions In points A Fixed support
Along line AA R_z, M_x and M_y fixed to impose 2D behaviour
Loads Along line AA Linear force of q=10kN/m which varies in time
Damping: 0.00%
Mesh No. of divisions 20


How to model this dynamic action?

  • The relation between the time and the amplitude of load is should be entered relative to the period T.
    t_1/t_2 = 0,4
  • The time-amplitude relation is scaled by defining t_2 as peroid.

Results

Eigen modes

The eigen modes are calculated using the modal mass due to the self-weight. The load q does not contribute to this.

Eigen mode Independent reference Diamonds Difference
1 63,01Hz 63,19Hz 0,29%

Dynamic response

Deformation \delta_y due to the dynamic load in Diamonds

Eigen mode Independent reference Diamonds Difference
1 2,469mm 2,467mm -0.08%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 03: poutre élancée encastrée-encastrée avec inerties différentes

  • Tested in Diamonds 2026.

]]> DLX 03: Planar frame – dynamic response https://support.buildsoft.eu/knowledge-base/validation-planar-frame-dynamic-response/ Wed, 01 Nov 2023 14:48:13 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=10425

Description

Material Modulus of elasticity E=200 000 N/mm^2
Density \rho=7800 kg/m^3
Poisson’s ratio \nu= 0.3
Geometry Cross-section Area A = 2872 mm^2
Moment of inertia I = 19 400 000 mm^4
Boundary conditions Points A Simple supports
Loads In point C Sinusoidal force with amplitude F=100kN and frequency of 12.732Hz

Damping: 5%
Mesh No. of divisions 20

Results

Eigen modes

Eigen mode1 Shape Independent reference Diamonds1 Difference
1 16.46Hz 16,33Hz -0,79%
2 38,17Hz 36,66Hz -3,96%


1 Only the modes relevant for the dynamic response are listed in this table

Dynamic response

Deformation \delta_y due to the dynamic load in Diamonds

Location Which result Independent reference Diamonds Difference
B Deformation \delta_y 98 mm 99,8mm 1.84%
C Deformation \delta_y 227 mm 225,2mm -0,79%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 08: grillage plan de poutres.

  • Tested in Diamonds 2026.

]]> DLX 06: Thin walled tube section – eigenfrequencies https://support.buildsoft.eu/knowledge-base/thin-walled-tube-section-eigen-frequencies/ Wed, 01 Nov 2023 14:04:25 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=10415

Description

Material Modulus of elasticity E=210 000 N/mm^2
Density \rho=7800 kg/m^3
Poisson’s ratio \nu= 0.3
Geometry Cross-section Tube d_e = 20mm and t = 2mm
Boundary conditions In point A & B Simple support
In point C & D Fixed support
Mesh No. of divisions 8

Results

Eigen mode Shape Independent reference Diamonds Difference
1 17,9Hz 17,7Hz -1,12%
2 24,8Hz 24,4Hz -1,61%
3 25,3Hz 25,0Hz -1,19%
4 27,0Hz 26,7Hz -1,11%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 14: modes de vibration d’un coude de tuyauterie mince.

  • Tested in Diamonds 2026.

]]> DLL 01: Slender short beam – simply supported – eigenfrequencies https://support.buildsoft.eu/knowledge-base/slender-short-beam-simply-supported-eigenfrequencies/ Tue, 31 Oct 2023 16:41:51 +0000 https://support.buildsoft.eu/?post_type=ht_kb&p=10395

Description

Material Modulus of elasticity E=200 000 N/mm^2
Density \rho=7800 kg/m^3
Poisson’s ratio \nu= 0.3
Geometry Cross-section Dimensions b = 100mm
h = 200 mm
Factor for shear \lambda = 1.5
Boundary conditions In point A Fixed support
In point B Roller support
Along line AB R_z, M_x and M_y fixed
to impose 2D behaviour
Mesh No. of divisions 40

Results

Eigen mode Shape Independent reference Diamonds Difference
1 – flexion 431,56Hz 433,51Hz 0,45%
2 – traction 1265,92Hz 1266,01Hz 0,01%
3 – flexion 1498,30Hz 1505,76Hz 0,5%
4 – flexion 2870,66Hz 2854,20Hz -0,57%
5 – traction 3797,77Hz 3799,97Hz 0,06%
6 – flexion 4377,84Hz 4280,76Hz -2,22%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 01: poutre courte sur appuis simples.

  • Tested in Diamonds 2026.

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