Analysis of an Axially Compressed Electric Welded Circular Hollow Section Column
Objective: Check the mode for calculating columns of solid cross-section in the “Steel” postprocessor of SCAD
Task: Check the design section of an axially compressed electric welded circular hollow section column with a height of 7,7 m.
Source: Kuznetsov A.F., Kozmin N.B., Amelkovich S.V. Examples of the analysis of steel structures of civil and industrial buildings. Textbook for students of construction specialties. - Chelyabinsk, 2009. – p. 11, 12.
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:
5.3 Column_Example_5.3.spr;
report – 5.3 Column_Example_5.3.doc
Initial data:
| l = 7,7 m | Column height |
| μ = 1,0 | The lower and upper restraints are pinned |
| N = 472,5 kN | Design compressive force |
| γc = 1 | Service factor |
| Ry = 23 kN/cm2 | Steel grade C235 |
|
A = 51.12 см2 |
Geometric properties of the selected section |
SCAD Results. STEEL Postprocessor:
[Element No. 1] Forces
|
N
Max. -48,17 T |
My Max. 0 T*m
Max. 0 T*m |
Mz Max. 0 T*m
Max. 0 T*m |
|
Mk Max. 0 T*m
Max. 0 T*m |
Qz Max. 0 T
Max. 0 T |
Qy Max. 0 T
Max. 0 T |
|
|
Length of the bar 7,7 m |
|
Analysis complies with SNiP II-23-81*
Structural member column1
Steel: C235
Member length 7,7 m
Limit slenderness for members in compression: 180 - 60α
Limit slenderness for members in tension: 300
Service factor 1
Importance factor 1
Effective length factor XoZ -- 1,0
Effective length factor XoY -- 1,0
Length between out-of-plane restraints 7,7 m
Section:
|
Results |
Check |
Utilization factor |
|---|---|---|
|
Sec. 5.24,5.25 |
Strength under combined action of longitudinal force and bending moments, no plasticity |
0,4 |
|
Sec. 5.3 |
Stability under compression in XoY (XoU) plane |
0,63 |
|
Sec. 5.3 |
Stability under compression in XoZ (XoV) plane |
0,63 |
|
Sec. 5.34 |
Stability under compression and bending in two planes |
0,63 |
|
Sec. 5.1 |
Strength under axial compression/tension |
0,4 |
|
Sec. 6.15,6.16 |
Limit slenderness in XoY plane |
0,62 |
|
Sec. 6.15,6.16 |
Limit slenderness in XoZ plane |
0,62 |
Utilization factor 0,63 - Stability under compression in XoY (XoU) plane
Manual calculation (SNiP II-23-81*):
1. Strength check of the selected column section:
\[ \frac{N}{AR_{y} \gamma_{c} }=\frac{472,5}{51,12\cdot 23\cdot 1}=0,402. \]
2. Slenderness of the column:
\[ \lambda_{y} =\frac{l_{ef,y} }{i_{y} }=\frac{1,0\cdot 7,7\cdot 100}{8,699}=88,516; \] \[ \lambda_{z} =\frac{l_{ef,z} }{i_{z} }=\frac{1,0\cdot 7,7\cdot 100}{8,699}=88,516. \]
3. Conditional slenderness of the column:
\[ \bar{{\lambda }}_{y} =\frac{l_{ef,y} }{i_{y} }\sqrt {\frac{R_{y} }{E}} =\frac{1,0\cdot 7,7\cdot 100}{8,699}\sqrt {\frac{230}{2,06\cdot 10^{5}}} =2,9577; \] \[ \bar{{\lambda }}_{z} =\frac{l_{ef,z} }{i_{z} }\sqrt {\frac{R_{y} }{E}} =\frac{1,0\cdot 7,7\cdot 100}{8,699}\sqrt {\frac{230}{2,06\cdot 10^{5}}} =2,9577. \]
4. Buckling coefficients at \(2,5<\bar{{\lambda }}\le 4,5\):
\[ \begin{array}{l} \varphi_{y} =\varphi_{z} =1,47-13,0\frac{R_{y} }{E}-\left( {0,371-27,3\frac{R_{y} }{E}} \right)\bar{{\lambda }}_{y} +\left( {0,0275-5,53\frac{R_{y} }{E}} \right)\bar{{\lambda }}_{y}^{2} = \\ =1,47-\frac{13,0\cdot 230}{2,06\cdot 10^{5}}-\left( {0,371-\frac{27,3\cdot 230}{2,06\cdot 10^{5}}} \right)\cdot 2,9577+\left( {0,0275-\frac{5,53\cdot 230}{2,06\cdot 10^{5}}} \right)\cdot 2,9577^{2}=0,6349. \\ \end{array} \]
5. Strength of the column from the condition of providing the general stability under axial compression:
\[ N_{b,y} =\varphi_{y} AR_{y} \gamma_{c} =0,6349\cdot 23\cdot 51,12\cdot 1=746,476 \quad kN; \] \[ N_{b,z} =\varphi_{z} AR_{y} \gamma_{c} =0,6349\cdot 23\cdot 51,12\cdot 1=746,476\quad kN. \]
6. Limit slenderness of the column:
\[ \left[ \lambda \right]_{y} =180-60\alpha_{y} =180-60\cdot \frac{N}{\varphi _{y} AR_{y} \gamma_{c} }=180-60\cdot \frac{472,5}{746,476}=142,022; \] \[ \left[ \lambda \right]_{z} =180-60\alpha_{z} =180-60\cdot \frac{N}{\varphi _{z} AR_{y} \gamma_{c} }=180-60\cdot \frac{472,5}{746,476}=142,022. \]
Comparison of solutions:
|
Factor |
Source |
Manual calculation |
SCAD |
Deviation, % |
|---|---|---|---|---|
|
Strength under combined action of longitudinal force and bending moments, no plasticity |
– |
0,402 |
0,4 |
0,0 |
|
Stability under compression in XoY (XoU) plane |
0,966 |
472,5/746,476 = 0,633 |
0,63 |
0,0 |
|
Stability under compression in XoZ (XoV) plane |
0,966 |
472,5/746,476 = 0,633 |
0,63 |
0,0 |
|
Strength under axial compression/tension |
0,511 |
0,402 |
0,4 |
0,0 |
|
Limit slenderness in XoY plane |
– |
88,516/142,022 = 0,62 |
0,62 |
0,0 |
|
Limit slenderness in XoZ plane |
– |
88,516/142,022 = 0,62 |
0,62 |
0,0 |