Description
A collar roof structure is loaded by three different load cases. The internal forces are calculated analytically and compared with RFEM 6.
Input Parameters and Structural System
The calculation is performed without considering self-weight and according to the linear static analysis. The shear stiffness of the cross-section is neglected.
| Beam geometry | Width / height | b/h | 6/18 | [cm] | |||||
| System geometry | Total length | L | 12 | [m] | |||||
| Length of collar beam | b | 4.5 | [m] | ||||||
| Height system | H | 4 | [m] | ||||||
| Height to collar beam | hu | 2.5 | [m] | ||||||
| Height from collar beam | ho | 1.5 | [m] | ||||||
| Rafter angle | a | 33.69 | [°] | ||||||
| Load situations | Distributed load – rafter | g | 5 | [kN] | |||||
| Distributed load – collar beam | gk | 5 | [kN] | ||||||
| Distributed load – wind load | gw | 5 | [kN] | ||||||
Analytical Solution
For the analytical solution, the formulas according to [1] were used for the collar roof.
Comparison of Analytical Solution with RFEM Solution
| Load Introduction 1 – Rafter | Comparison value | Analytical Solution | RFEM 6 | Difference |
|---|---|---|---|
| Az | 30.00 [kN] | 30.00 [kN] | 0.00 [%] |
| Ax | 33.61 [kN] | 33.56 [kN] | 0.15 [%] |
| N | -29.63 [kN] | -29.48 [kN] | 0.51 [%] |
| M | -6.68 [kNm] | -6.56 [kNm] | 2.10 [%] |
| Load Introduction 2 – Collar Beams | Comparison value | Analytical Solution | RFEM 6 | Difference |
|---|---|---|---|
| Az | 11.25 [kN] | 11.25 [kN] | 0.00 [%] |
| Ax | 16.88 [kN] | 16.84 [kN] | 0.24 [%] |
| N | -16.88 [kN] | -16.79 [kN] | 0.53 [%] |
| M | 0.00 [kNm] | 0.00 [kNm] | 0.00 [%] |
| Load Introduction 3 – Wind Load | Comparison value | Analytical Solution | RFEM 6 | Difference |
|---|---|---|---|
| Az | 19.17 [kN] | 19.17 [kN] | 0.00 [%] |
| Bz | 10.83 [kN] | 10.83 [kN] | 0.00 [%] |
| Ax | 4.27 [kN] | 4.24 [kN] | 0.70 [%] |
| Bx | 24.27 [kN] | 24.24 [kN] | 0.12 [%] |
| N | -21.40 [kN] | -21.20 [kN] | 0.93 [%] |
| M2 | 10.41 [kNm] | 10.60 [kNm] | 1.83 [%] |
| M4 | -20.06 [kNm] | -19.88 [kNm] | 0.90 [%] |
The analytical calculation corresponds with the results from RFEM 6. The largest relative difference is 2.1%.
Literature
[1] Schneider, K.-J. (2012). (2016). Schneider – Bautabellen für Ingenieure, (22nd Mit Berechnungshinweisen und Beispielen (A. Albert, ed.; 20th ed.)
