Analysis of a Purlin for Biaxial Bending
Objective: Check the calculation of continuous purlins.
Task: Verify the correctness of the strength analysis and the calculation of the deflection of the element.
References: Nasonov S.B. Manual on design and analysis of building structures. – M: ASV Publishing House, 2013. – p. 86-88.
Initial data file:
Example 11.SAV;
report – Decor 11.doc.
Software version: DECOR 21.1.1.1, 27.05.2016.
Compliance with the codes: SNiP ІІ-25-80, SP 64.13330.2011.
Initial data from the source:
| b×h = 15×20 cm | Section sizes of the element |
| l = 4,2 m | Purlin span |
| μx = μy = 1 | Effective length factors |
| qэкн = 3,0 kN/m | Uniformly distributed serviceability load (characteristic value) |
| qэкр = 3,5 kN/m | Uniformly distributed serviceability load (design value) |
| α = 30° | Purlin inclination |
| Material of the element: | pine |
| Grade of wood: | 2 |
| Operating conditions class: | 1 (А2 according to SNiP ІІ-25-80). |
DECOR initial data:
Importance factor γn = 1
Importance factor (serviceability limit state) = 1
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Service factors |
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Service factor for temperature and humidity operating conditions mВ |
1 |
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Allowance for the temperature conditions of operation mТ |
1 |
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Allowance for the duration of loading md |
1 |
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Service factor under short-term loads mn |
1 |
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Factor that allows for the effect of impregnation with protective substances mа |
1 |
Wood species - Pine
Grade of wood - 2
Density of wood 5 kN/m3
Structure
Spacing of bracing in the roof plane 0,6 m
Roof inclination 30 degrees
Section
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Non-glued timber section
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Load case 1 - permanent
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Load type |
Value |
Dead weight factor |
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|---|---|---|---|
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span 1, length = 4,2 m |
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3,5 |
kN/m |
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Load case 1 - permanent Safety factor for load: 1,16667 |
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Load case 2 - permanent
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Load type |
Value |
Dead weight factor |
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|---|---|---|---|
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|
0,15 |
kN/m |
1,1 |
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Load case 2 - permanent Safety factor for load: 1,1 |
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Support reactions |
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|---|---|---|
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Force in support 1 |
Force in support 2 |
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kN |
kN |
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by criterion Mmax |
7,697 |
7,697 |
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by criterion Mmin |
7,697 |
7,697 |
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by criterion Qmax |
7,697 |
7,697 |
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by criterion Qmin |
7,697 |
7,697 |
Comparison of solutions:
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File |
Example 11.SAV |
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Report file |
Decor 11.doc |
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Check |
Strength of the member under the bending moment My |
Deflection |
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Theory |
1,24/1,5 = 0,827 |
1,59/2,1 = 0,757 |
|
DECOR |
0,826 |
0,775 |
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Deviation, % |
0,115% |
2,36% |
Comments:
- Maximum allowable deflection for purlins is determined as (1/200)l = 0,005l (table 16 of SNiP ІІ-25-80, table 19 of SP 64.13330.2011).
- Spacing of bracing in the roof plane has to be specified in DECOR. Since it is not determined in the problem, the value of 0,6 m is used.
- The density of pine at the operating conditions class 1 (А2) is equal to ρ = 500 kg/m3 = 5 kN/m3 (Annex 3 of SNiP ІІ-25-80, Annex E of SP 64.13330.2011).
- The loads in DECOR are specified in the following way:
- Load case 1 – external load (design value) 3,5 kN/m with a safety factor for load equal to qsd / qsch = 3,5/3,0 = 1,16667;
- Load case 2 – load from the self-weight with a dead weight factor of 1,1 and a safety factor for load of 1,1.
- The difference in the deflection of 2,36% was obtained due to the fact that shear was not taken into account in the calculation in the theoretical source.