VE9956 | Internal Forces of Collar Roof

Description

A collar beam roof truss is stressed by three different load cases. The internal forces are calculated analytically and compared using RFEM 6.

Input Parameters and Structural System

The calculation is performed without considering self-weight and according to 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]
	Collar Beam Length	b	4.5	[m]
	System Height	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

Formulas from [1] were applied to the collar roof for the analytical solution.

Comparison of Analytical Solution with RFEM Solution

Load Attack 1 Rafter
Comparison Value	Analytical Solution	RFEM 6	Deviation
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 Attack 2 Collar Beam
Comparison Value	Analytical Solution	RFEM 6	Deviation
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 Attack 3 Wind Load
Comparison Value	Analytical Solution	RFEM 6	Deviation
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 well with the results from RFEM 6. The greatest relative deviation is 2.1%.

Literature

[1] Schneider, K.-J. (2012). Schneider - Bautabellen für Ingenieure: Mit Berechnungshinweisen und Beispielen, (20th ed.). A. Albert, Hrsg.

;