Analysis of a Top Truss Chord from Unequal Angles
Objective: Check the mode for calculating truss members in the “Steel” postprocessor of SCAD
Task: Check the top truss chord section from two unequal angles L160x100x9 mm. The truss panel length is 2,58 m. The truss is restrained out of the bending plane through the panel.
Source: Steel Structures: Student Handbook / [Kudishin U.I., Belenya E.I., Ignatieva V.S and others] - 13-th ed. rev. - M.: Publishing Center "Academy", 2011. p. 280.
Compliance with the codes: SNiP II-23-81*, SP 16.13330.2011, DBN B.2.6-163:2010, DBN B.2.6-198:2014.
Initial data file:
7.1 Truss_Element_Example_7.1.spr;
report – 7.1 Truss_Element_Example_7.1.doc
Initial data:
| N = 535 kN | Design compressive force |
| Ry = 24 kN/cm2 | Steel grade C245 |
| γc = 0,95 | Service factor |
| g = 12 mm | Thickness of the gusset plate |
| ly = 2,58, lz = 5,16 | Effective lengths of the bar |
| iy = 2,851 cm, А = 45,74 cm2 | Geometric properties of |
| iz = 7,745 cm | the top chord section from two angles 160х100х9 |
SCAD Results. STEEL Postprocessor:
[Element No 1] Forces
|
N
Max. -535 kN |
My Max. 0 kN*m
Max. 0 kN*m |
Mz Max. 0 kN*m Snap 0 m
Max. 0 kN*m |
|
Mk Max. 0 kN*m
Max. 0 kN*m |
Qz Max. 0 kN
Max. 0 kN |
Qy Max. 0 kN
Max. 0 kN |
|
|
Length of the bar 2,58 m |
|
Analysis complies with SNiP II-23-81*
Structural member Truss chord
Steel: C245
Member length 2,58 m
Limit slenderness for members in compression: 180 - 60α
Limit slenderness for members in tension: 300
Service factor 0,95
Importance factor 1
Inelasticity is forbidden
Effective length factor in the X1OZ1 plane 1
Effective length factor in the X1OY1 plane 2
Length between the restraints out of the bending plane 2,58 m
Section:
Profile: Unequal angle GOST 8510-86* L160x100x9
|
Results |
Check |
Utilization factor |
|---|---|---|
|
Sec.5.24,5.25 |
Strength under combined action of longitudinal force and bending moments, no plasticity |
0,51 |
|
Sec.5.3 |
Stability under compression in XoY (XoU) plane |
0,66 |
|
Sec.5.3 |
Stability under compression in XoZ (XoV) plane |
0,84 |
|
Sec.5.1 |
Strength under axial compression/tension |
0,51 |
|
Sec.6.15,6.16 |
Limit slenderness in XoY plane |
0,48 |
|
Sec.6.15,6.16 |
Limit slenderness in XoZ plane |
0,7 |
Utilization factor 0,84 - Stability under compression in XoZ (XoV) plane
Manual calculation (SNiP II-23-81*):
1. Strength check
\[ \frac{N}{A}=\frac{535}{45,74}=11,69655\ kN/cm^{2}< R_y\gamma_c=24\cdot 0,95=22,8\ kN/cm^2\]
2. Slenderness of the truss member:
\[ \lambda_{y} =\frac{l_{ef,y} }{i_{y} }=\frac{2,58\cdot 100}{2,851}=90,49456; \] \[ \lambda_{z} =\frac{l_{ef,z} }{i_{z} }=\frac{5,16\cdot 100}{7,745}=66,6236. \]
3. Conditional slenderness of the truss member:
\[ \bar{{\lambda }}_{y} =\frac{l_{ef,y} }{i_{y} }\sqrt {\frac{R_{y} }{E}} =\frac{2,58\cdot 100}{2,851}\sqrt {\frac{240}{2,06\cdot 10^{5}}} =3,0888; \] \[ \bar{{\lambda }}_{z} =\frac{l_{ef,z} }{i_{z} }\sqrt {\frac{R_{y} }{E}} =\frac{5,16\cdot 100}{7,745}\sqrt {\frac{240}{2,06\cdot 10^{5}}} =2,274. \]
4. Buckling coefficients:
\[ \bar{{\lambda }}_{y} =\frac{l_{ef,y} }{i_{y} }\sqrt {\frac{R_{y} }{E}} =\frac{2,58\cdot 100}{2,851}\sqrt {\frac{240}{2,06\cdot 10^{5}}} =3,0888; \] \[ \bar{{\lambda }}_{z} =\frac{l_{ef,z} }{i_{z} }\sqrt {\frac{R_{y} }{E}} =\frac{5,16\cdot 100}{7,745}\sqrt {\frac{240}{2,06\cdot 10^{5}}} =2,274. \]
5. Strength of the truss member from the condition of providing the general stability under axial compression:
\[ N_{b,y} =\varphi_{y} AR_{y} \gamma_{c} =0,60805\cdot 45,74\cdot 24\cdot 0,95=634,118 kN; \] \[ N_{b,z} =\varphi_{z} AR_{y} \gamma_{c} =0,77176\cdot 45,74\cdot 24\cdot 0,95=804,847 kN. \]
6. Limit slenderness of the truss member:
\[ \left[ \lambda \right]_{y} =180-60\alpha_{y} =180-60\cdot \frac{N}{\varphi _{y} AR_{y} \gamma_{c} }=180-60\cdot \frac{535}{634,118}=129,3785; \] \[ \left[ \lambda \right]_{z} =180-60\alpha_{z} =180-60\cdot \frac{N}{\varphi _{z} AR_{y} \gamma_{c} }=180-60\cdot \frac{535}{804,847}=140,1166. \]
Comparison of solutions:
|
Factor |
Source |
Manual calculation |
SCAD |
Deviation, % |
|---|---|---|---|---|
|
Strength of member |
535/45,8/22,8=0,512 |
11,6966/22,8 = 0,513 |
0,51 |
0,0 |
|
Stability of member in the truss plane |
21,4/22,8=0,938 |
535/634,118 = 0,844 |
0,84 |
0,0 |
|
Stability of member out of the truss plane |
not defined |
535/804,847 = 0,665 |
0,66 |
0,0 |
|
Slenderness of the member in the truss plane |
not defined |
90,4946/129,3785 = 0,7 |
0,7 |
0,0 |
|
Slenderness of the member out of the truss plane |
not defined |
66,6236/140,1166 = 0,4755 |
0,48 |
0,0 |
Comments:
In the source the buckling coefficient for the conditional slenderness of the bar of 3.09 was mistakenly taken as 0.546 instead of 0.6081, which caused the differences in the results of the stability analysis.