VE9956 | Internal Forces of Collar Roof

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]

VE 009956 | Collar Roof: Structural System, Dimensions, and Load Application 1

VE9956 Collar Roof: Load Applications 2 and 3

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.)

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