Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes

Transcription

1 Autodesk Robot Stutual Analysis Pofessional VERIFICATIO MAUAL FOR ITALIA CODES Mah 2014

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3 ITRODUCTIO... 1 COCRETE DM 9/1/96 RC COLUMS... 3 VERIFICATIO EXAMPLE 1 - COLUM SUBJECTED TO AXIAL LOAD AD BIAXIAL BEDIG... 4 LITERATURE Mah 2014 page i

4 ITRODUCTIO This veifiation manual ontains numeial examples fo RC olumns pepaed and alulated by Autodesk Robot Stutual Analysis Pofessional vesion The ompaison of esults is still valid fo the next vesions. All examples have been taken fom handbooks that inlude benhmak tests oveing fundamental types of behaviou enounteed in stutual analysis. Benhmak esults (signed as Handbook ) ae ealled, and ompaed with esults of Autodesk Robot Stutual Analysis Pofessional (signed futhe as Robot ). Eah poblem ontains the following pats: - title of the poblem - speifiation of the poblem - Robot solution of the poblem - outputs with alulation esults and alulation notes - ompaison between Robot esults and exat solution - onlusions. Mah 2014 page 1 / 10

5 COCRETE Mah 2014 page 2 / 10

6 1. DM 9/1/96 RC olumns Mah 2014 page 3 / 10

7 VERIFICATIO EXAMPLE 1 - Column subjeted to axial load and biaxial bending DESCRIPTIO OF THE EXAMPLE: Following example illustates the poedue of dimensioning of biaxial bending of olumn, whih is non-sway in one dietion, wheeas sway in the othe. The esults of the pogam ae aompanied by the manual alulations. 1. SECTIO DIMESIOS 2. MATERIALS Conete : R20 Rk = (MPa) Longitudinal einfoement : FeB44k fyk = (MPa) Tansvesal einfoement : FeB32k fyk = (MPa) 3. BUCKLIG MODEL As an be seen the sway olumn is assumed fo Z dietion, and the non-sway olumn fo Y dietion. Mah 2014 page 4 / 10

8 4. LOADS OTE: Let us assume, the moments in Y dietion ae linealy distibuted along the height of the olumn. Thus, we define only the ends moments fo Y dietion. In Z dietion howeve, we assume the mid-height moment is not a esult of the linea distibution. Fo suh a ase, Robot let the use define the moments in the mid-setion expliitly. 5. CALCULATED REIFORCEMET: Pogam geneates the einfoement RESULTS OF THE SECTIO CALCULATIOS: The dimensioning ombination is 1.4DL1+1.0LL1 The dimensioning setion (whee the most unfavoable set of foes is found) is fo that ombination the setion in the mid-height of the olumn (maked as (C)). Mah 2014 page 5 / 10

9 Sine the olumn is found as slende, the seond-ode effets ae taken into aount in both dietions. In paallel the othe setions (at the ends of the olumn) ae heked fo all ombinations of loads. In the top and bottom ends setions of the olumn in Y dietion, the influene of bukling has not been taken into aount, sine the stutue is non-sway in this dietion. In Z dietion howeve, the influene of slendeness is taken into aount fo all thee setions of the olumn. All the esults of al foes fo eah ombination and eah setion of the olumn may be seen in the table Intesetion at the Column-esults layout. 7. CALCULATIOS OF TOTAL MOMET: 7.1. LOADS Fo the dimensioning ombination, the loads ae: Case MyA MyB MyC MzA MzB (k) (k*m) (k*m) (k*m) (k*m) (k*m) 1 DL * 2 LL * Dimensioning ombination MzC (k*m) 1.4DL1+1.0LL whee A, B and C denote uppe, lowe and mid-height setions of the olumn espetively. * - the values ae witten by hand by the use (see point 4 Loads) Mah 2014 page 6 / 10

10 7.2. THE IFLUECE OF SLEDERESS Two independent alulations of the al moment fo both dietions ae aied out. As a fist step, it is heked, if d max (aoding to point a) d f d A f A OK max max (k) Y DIRECTIO Slendeness analysis: l 0 = i Chek if * aoding to * d / A As A = = 1.68 % A = 0.24 m 2 Sine * the olumn is found as slende fo Y dietion. The abovementioned slendeness means that the al eentiity of the axial foe in Z ( M ) dietion will be: z y / ' a OTE: If the olumn is found as non-slende ( *), the al eentiity would be ' a. Chek if the method of slendeness analysis is appliable ( 3 *) * - OK Calulation of initial eentiity Fo the mid-height setion, we have: ' = (m) > = (m) Calulation of additional eentiity a a max 2m; = (m), 300 l = 8.0 (m) 0 l 0 Mah 2014 page 7 / 10

11 Calulation of seond-ode eentiity 2 l = (m) 1 1 K K = K 0 f d E d = (m) E s = 200 (GPa) s = f = 374 (MPa) max( 1;1 ) - if eep oeffiient >2 and 75 and ' h eff long f k eff K 1 - in othe ases Thus, we have K K 1 ud d = ud bal ud bal f A f A = (k) d d 0. 4 f A = (k) The al eentiity in Z dietion: ' = (m) The al moment My : 285 (km) M y e Z DIRECTIO Slendeness analysis: l 0 = i Chek if * aoding to * d / A = a Mah 2014 page 8 / 10

12 A s = 1.68 % A A = 0.24 m 2 Sine * the olumn is found as slende fo Z dietion. The abovementioned slendeness means that the al eentiity of the axial foe in Y ( M ) dietion will be: y z / ' a OTE: If the olumn is found as non-slende ( *), the al eentiity would be ' a. Chek if the method of slendeness analysis is appliable ( 3 *) * - OK Calulation of initial eentiity Fo the mid-height setion, we have: ' M ( C) / = (m) (the moment in mid-height setion is given dietly by the use) z d Calulation of additional eentiity a a max 2m; = (m), 300 l = 5.2 (m) 0 l 0 Calulation of seond-ode eentiity 2 l = (m) 1 1 K K = K 0 f d E d = (m) E s = 200 (GPa) s = f = 374 (MPa) max( 1;1 ) - if eep oeffiient >2 and 75 and ' h eff long eff Mah 2014 page 9 / 10

13 f k K 1 - in othe ases Thus, we have K K 1 ud d = ud bal ud bal The al eentiity in Z dietion: f A f A = (k) d d 0. 4 f A = (k) ' = (m) The al moment My : 150 (km) M z e 7.3. FIAL RESULT a M = 285 (km) y M = 150 (km) z 8. COCLUSIOS The algoithm of alulations of the al moments (i.e. slendeness effets) in non-sway/sway olumn has been pesented. The esults obtained with the pogam (see point 6 Results of the Setion Calulations) ae in ageement with the manual alulations (see point 7.3 Final Result). LITERATURE [1] B.A.E.L. 91. Règles tehniques de oneption et de alul des ouvages et onstutions en béton amé suivant la méthode des états-limites. Mod. 99. [2] J. Pehat, Patique du BAEL 91, Deuxième èdition, Eyolles, 1998, Example 2, pp. 98 [3] J-P. Mougin, Béton Amé. BAEL 91 et DTU assoiés, Eyolles, 1995, Example 1, pp. 113 Mah 2014 page 10 / 10