Eurocode 3. Example 6.9: Member resistance under combined major axis bending and axial compression

In this article we compare the resistance under combined major axis bending and axial compression according to SDC Verifier and Designer’s Guide to Eurocode3: Design of steel buildings EN 1993-1-1.

All results are generated with SDC Verifier 5.3 and calculated with FEMAP v2019.1.

Task:

A rectangular hollow section (RHS) member is to be used as a primary floor beam of 7.2 m span in a multi-storey building. Two design point loads of 58 kN are applied to the primary beam (at locations B and C) from secondary beams, as shown in Figure 6.27. The secondary beams are connected through fin plates to the webs of the primary beam, and full lateral and torsional restraint may be assumed at these points. The primary beam is also subjected to a design axial force of 90 kN.
Assess the suitability of a hot-rolled 200 100 16 RHS in grade S355 steel for this application.

Solution:

Model

Materials

Title	Young Modulus [MPa]	Shear Modulus [MPa]	Poisson Ratio	Shear [MPa]	Mass Density [t/mm^3]	Tensile Strength [MPa]	Yield Stress [MPa]
1..S355	2.10e+5	0	0.3000	0	7.850e-09	455.0	355.0

Property “1..RHS 200x100x16”

Property	Value	Property Shape
Type / Elements	Beam / 30
Material	1..S355
Mass [t]	0.5
Gravity Center [mm]	[3600.00; 0.00; 10.00]
Area, [mm^2]	8300.0000
I1, [mm^4]	11470000.00
I2, [mm^4]	36780000.00
I12, [mm^4]	0
Torsion Constant, [mm^4]	29820000.00
Y Shear Area, [mm^2]	2150.1420
Z Shear Area, [mm^2]	5779.1710
Nonstructural Mass, [t]	0
Perimeter, [mm]	600.00
Warping Constant, [mm^6]	0
Y Neutral Axis Offset A, [mm]	0
Z Neutral Axis Offset A, [mm]	0
h [mm]	200.000
w [mm]	100.000
t [mm]	16.000

Boundary Conditions

Load “1..Shear Y = -58kN”

Definition	Load Type	Applied On	Values
Force on Node	Force	Nodes: 42, 53	(0; -58000; 0)

Load “2..Axial = 90kN”

Definition	Load Type	Applied On	Values
Force on Node	Force	Nodes: 64	(-90000; 0; 0)

Constraint “1..fixed”

Definition	Count	DOF
Constraint on Node	Nodes: 22	Tx Ty Tz Rx
Constraint on Node	Nodes: 64	Ty Tz Rx

Cross-section classification

Property		Epsilon	Lambda Flange	Limit1		Limit2		Limit3	Class
Check	[S2] 6..Flange Classification
1..RHS 200 x 100 x 16		0.81	3.25	26.85		30.92		34.17	1.0000

Components		Alpha Web	Phi	Lambda Web		Limit1 Web	Limit2 Web		Limit3 Web	Web Class	Class
Check	[S2] 7..Classificaton				Load Set			LS1..Shear + Axial
Selection	Beam Member 2
Beam Member 2		0.52	-0.93	9.5000		55.18	63.54		94.88	1.00	1.00

Compresson resistance

Components		Axial Force [KN]	Design Tension Resistance [KN]		Design Compression Resistance [KN]		Design Resistance [KN]	Utilization Factor
Check	[S2] 9..Axial Check			Load Set		LS1..Shear + Axial
Selection	Beam Member 2
Beam Member 2		-90.0	2946.5		2946.5		2946.5	0.03

Bending resistance

Components		Bending Moment Y [KN mm]	Bending Moment Z [KN mm]	Bending Moment Resistance Y [KN mm]		Bending Moment Resistance Z [KN mm]		Utilization Factor Y	Utilization Factor Z	Utilization Factor
Check	[S2] 10..Bending Check				Individual Load		IL1..Shear Y = -58kN.fixed
Selection	Beam Member 2
Beam Member 2		0.0e+3	-139.2e+3	103.0e+3		174.3e+3		0.00	0.80	0.80

Note: Section Plastic Modulus in SDC Verifier was adjusted using characteristic to match the section with fillets:

6..User Plastic Section Modulus Y

Property	Value
Type	Property ‘6..User Plastic Section Modulus Y’
Alias	WplYUser
1..RHS 200 x 100 x 16	290000

7..User Plastic Section Modulus Z

Property	Value
Type	Property ‘7..User Plastic Section Modulus Z’
Alias	WplZUser
1..RHS 200 x 100 x 16	491000

Shear Resistance

Components		Shear Force Y [KN]	Shear Force Z [KN]	Shear Force Y Resistance [KN]	Shear Force Z Resistance [KN]	Utilization Factor Y		Utilization Factor Z	Utilization Factor	YieldReduced [MPa]
Check	[S2] 8..Shear Check				Load Set		LS1..Shear + Axial
Selection	Beam Member 2
Beam Member 2		0.0	58.0	567.1	1134.1	0.00		0.05	0.05	355.0

Buckling resistance in compression

Components		Ncr_y [KN]	Ncr_z [KN]	Lambda Y	Lambda Z		Fy	Fz		Xi_Y	Xi_Z	Nb Rd Y [KN]
Check	[S2] 12..Buckling Compression					Load Set			LS1..Shear + Axial
Selections	2
Beam Member 2		4127.2	1470.5	0.8449	1.4155		0.92	1.63		0.77	0.41	2266.0

Components		Lambda Y	Lambda Z	Fy		Fz	Xi_Y		Xi_Z	Nb Rd Y [KN]	Nb Rd Z [KN]
Check	[S2] 12..Buckling Compression				Load Set			LS1..Shear + Axial
Selections	2
Beam Member 2		0.8449	1.4155	0.92		1.63	0.77		0.41	2266.0	1209.2

Components		Lambda Y	Lambda Z	Fy		Fz	Xi_Y		Xi_Z	Nb Rd Y [KN]	Nb Rd Z [KN]
Check	[S2] 12..Buckling Compression				Load Set			LS1..Shear + Axial
Selections	2
Beam Member 2		0.8449	1.4155	0.92		1.63	0.77		0.41	2266.0	1209.2

Member buckling resistance in buckling

Components		L_LT [mm]	C1	Gm		Mcr [KN mm]	Lambda_LT		X_LT	Mb_Rd [KN mm]	Uf b
Check	[S2] 14..Lateral torsional buckling				Individual Load			IL1..Shear Y = -58kN.fixed
Selection	Beam Member 2
Beam Member 2		2400.000	1.000	80769.23		3152.9e+3	0.235		0.973	169.5e+3	0.82

Note: SDC Verifier does not apply rule λ<= λLT0, in results the Utilization is higher on 2% (0.82 vs 0.8).

Combined bending and axial compression part is not compared because Example uses alternative method 1 (Annex A) and SDC Verifier uses alternative method 2 (Annex B).

Results for member resistance under combined major axis bending and axial compression in SDC Verifier match with results in example 6.9.

Check other comparation of Eurocode3 design examples standard and SDC Verifier.

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