Check of a Section of a Flexural Member
Objective: Check of the beam analysis.
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. 80-82.
Initial data file:
Example 9.SAV;
report – Decor 9.doc.
Compliance with the codes: SNiP ІІ-25-80, SP 64.13330.2011.
Initial data from the source:
| b×h = 10×15 cm | Section sizes of the element |
| l = 3 m | Member length |
| μx = μy = 1 | Effective length factors (Fig. 1) |
| qэкн = 3,1 kN/m | Uniformly distributed characteristic serviceability load |
| qэкр = 3,7 kN/m | Uniformly distributed design serviceability load |
Material of the element: pine.
Grade of wood: 2.
Operating conditions class: 1 (А2 according to SNiP ІІ-25-80).
The beam is restrained out of the bending plane along the whole length of the compressed chord.
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:
Restraints against lateral displacements and rotations:
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Left |
Right |
|---|---|---|
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Displacement along Y |
Restrained |
Restrained |
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Displacement along Z |
Restrained |
Restrained |
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Rotation about Y |
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Rotation about Z |
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Continuous restraint of the compressed section elements out of the bending plane
Section:
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b = 100 mm 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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length = 3 m |
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3,7 |
kN/m |
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Load case 1 - permanent Safety factor for load: 1,19355 |
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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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0,075 |
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 |
5,674 |
5,674 |
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by criterion Mmin |
5,674 |
5,674 |
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by criterion Qmax |
5,674 |
5,674 |
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by criterion Qmin |
5,674 |
5,674 |
Comparison of solutions:
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File |
Example 9SAV |
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Report file |
Decor 9.doc |
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Check |
Strength of the member under the bending moment |
Strength under the lateral force |
Deflection |
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Theory |
1,14/1,3 = 0,877 |
0,057/0,16 = 0,356 |
1,19/1,2 = 0,992 |
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DECOR |
0,873 |
0,355 |
1,04 |
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Deviation, % |
0,463% |
0,46% |
4,62% |
Comments:
- Maximum allowable deflection for interstorey floor beams is determined as (1/250)l = 0,004l (table 16 of SNiP ІІ-25-80, table 19 of SP 64.13330.2011).
- The loads in DECOR are specified in the following way:
- Load case 1 – external load (design value) 3,7 kN/m with a safety factor for load equal to qsd / qsch = 3,7/3,1 = 1,19355;
- 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 4,62% was obtained due to the fact that the effect of shear is not taken into account in the calculation in the source.