® Autodesk ™ Robot Structural Analysis Professional VERIFICATION MANUAL FOR ITALIAN CODES March 2014 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes INTRODUCTION ..............................................................................................................................................................................1 CONCRETE .....................................................................................................................................................................................2 1. DM 9/1/96 – RC COLUMNS.........................................................................................................................................................3 VERIFICATION EXAMPLE 1 - COLUMN SUBJECTED TO AXIAL LOAD AND BIAXIAL BENDING ..............................................................4 LITERATURE .............................................................................................................................................................................10 March 2014 page i Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes INTRODUCTION This verification manual contains numerical examples for RC columns prepared and calculated by Autodesk Robot Structural Analysis Professional version 2013. The comparison of results is still valid for the next versions. All examples have been taken from handbooks that include benchmark tests covering fundamental types of behaviour encountered in structural analysis. Benchmark results (signed as “Handbook”) are recalled, and compared with results of Autodesk Robot Structural Analysis Professional (signed further as “Robot”). Each problem contains the following parts: - title of the problem - specification of the problem - Robot solution of the problem - outputs with calculation results and calculation notes - comparison between Robot results and exact solution - conclusions. March 2014 page 1 / 10 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes CONCRETE March 2014 page 2 / 10 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes 1. DM 9/1/96 – RC columns March 2014 page 3 / 10 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes VERIFICATION EXAMPLE 1 - Column subjected to axial load and biaxial bending DESCRIPTION OF THE EXAMPLE: Following example illustrates the procedure of dimensioning of biaxial bending of column, which is non-sway in one direction, whereas sway in the other. The results of the program are accompanied by the „manual‟ calculations. 1. SECTION DIMENSIONS 2. MATERIALS Concrete Longitudinal reinforcement Transversal reinforcement 3. : R20 : FeB44k : FeB32k Rck = 24.10 (MPa) fyk = 430.00 (MPa) fyk = 315.00 (MPa) BUCKLING MODEL As can be seen the sway column is assumed for Z direction, and the non-sway column for Y direction. March 2014 page 4 / 10 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes 4. LOADS NOTE: Let us assume, the moments in Y direction are linearly distributed along the height of the column. Thus, we define only the ends‟ moments for Y direction. In Z direction however, we assume the mid-height moment is not a result of the linear distribution. For such a case, Robot let the user define the moments in the mid-section explicitly. 5. CALCULATED REINFORCEMENT: Program generates the reinforcement 20 16. 6. RESULTS OF THE SECTION CALCULATIONS: The dimensioning combination is 1.4DL1+1.0LL1 The dimensioning section (where the most unfavorable set of forces is found) is for that combination the section in the mid-height of the column (marked as (C)). March 2014 page 5 / 10 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes Since the column is found as slender, the second-order effects are taken into account in both directions. In parallel the other sections (at the ends of the column) are checked for all combinations of loads. In the top and bottom ends‟ sections of the column in Y direction, the influence of buckling has not been taken into account, since the structure is non-sway in this direction. In Z direction however, the influence of slenderness is taken into account for all three sections of the column. All the results of total forces for each combination and each section of the column may be seen in the table “Intersection” at the Column-results layout. 7. CALCULATIONS OF TOTAL MOMENT: 7.1. LOADS For the dimensioning combination, the loads are: DL1 LL1 N (kN) 400 150 MyA (kN*m) 150 120 MyB (kN*m) 30 30 MyC (kN*m) 102 84 MzA (kN*m) 20 10 MzB (kN*m) 30 20 MzC (kN*m) 50* 40* 1.4DL1+1.0LL1 710 330 72 226.8 38 62 110 Case 1 2 Dimensioning combination where A, B and C denote upper, lower and mid-height sections of the column respectively. * - the values are written “by hand” by the user (see point 4 – Loads) March 2014 page 6 / 10 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes 7.2. THE INFLUENCE OF SLENDERNESS Two independent calculations of the total moment for both directions are carried out. As a first step, it is checked, if N d N max (according to point 4.2.1.2.a) f cd Ac f yd A 3863.68 (kN) 1.25 N d 710 3864 N max - OK N max Y DIRECTION Slenderness analysis: l0 = 46.19 i Check if * according to 4.2.4.2. 1 15 = 43.65 Nd / Ac A s = 1.68 % Ac Ac = 0.24 m2 * 60 Since * the column is found as slender for Y direction. The abovementioned slenderness means that the total eccentricity of the axial force in Z ( c z M y / N ) direction will be: ctot c'ca NOTE: If the column is found as non-slender ( * ), the total eccentricity would be ctot c'ca . Check if the method of slenderness analysis is applicable ( 46.19 130.95 3 * 3 * ) - OK Calculation of initial eccentricity c’ For the mid-height section, we have: c' 0.4 c1 0.6 c2 = 0.319 (m) > 0.4 c2 = 0.186 (m) Calculation of additional eccentricity ca l c a max 2cm; 0 = 0.027 (m), 300 l0 = 8.0 (m) March 2014 page 7 / 10 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes Calculation of second-order eccentricity 2 l 1 = 0.055 (m) 0 10 r 1 1 K r K = 0.00861 r r0 f yd 1 = 0.0075 r0 0.45 d E s d = 0.554 (m) Es = 200 (GPa) f yd = 374 (MPa) K max(1;1 eff ) eff N long N tot 0.35 >2 and 75 and c' h f ck 200 150 K 1 - in other cases Thus, we have Kr - if creep coefficient K 1 N ud N d = 1.181 N ud N bal N ud f cd Ac f yd A = 4503.59 (kN) N bal 0.4 f cd Ac = 1200.00 (kN) The total eccentricity in Z direction: ctot c'ca = 0.401 (m) The total moment My : M y N etot 285 (kNm) Z DIRECTION Slenderness analysis: l0 = 45.03 i Check if * according to 4.2.4.2. * 60 1 15 = 43.65 Nd / Ac March 2014 page 8 / 10 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes As = 1.68 % Ac Ac = 0.24 m2 Since * the column is found as slender for Z direction. The abovementioned slenderness means that the total eccentricity of the axial force in Y ( c y M z / N ) direction will be: ctot c'ca NOTE: If the column is found as non-slender ( * ), the total eccentricity would be ctot c'ca . Check if the method of slenderness analysis is applicable ( 45.03 130.95 3 * 3 * ) - OK Calculation of initial eccentricity c’ For the mid-height section, we have: c' M z (C ) / N d = 0.155 (m) (the moment in mid-height section is given directly by the user) Calculation of additional eccentricity ca l c a max 2cm; 0 = 0.020 (m), 300 l0 = 5.2 (m) Calculation of second-order eccentricity 2 l 1 0 = 0.036 (m) 10 r 1 1 K r K = 0.01348 r r0 f yd 1 = 0.0117 r0 0.45 d E s d = 0.354 (m) Es = 200 (GPa) f yd = 374 (MPa) K max(1;1 eff ) eff March 2014 N long N tot - if creep coefficient >2 and 75 and c' h page 9 / 10 Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes 0.35 f ck 200 150 K 1 - in other cases Thus, we have Kr K 1 N ud N d = 1.1483 N ud N bal N ud f cd Ac f yd A = 4503.59 (kN) N bal 0.4 f cd Ac = 1200.00 (kN) The total eccentricity in Z direction: ctot c'ca = 0.211 (m) The total moment My : M z N etot 150 (kNm) 7.3. FINAL RESULT M y = 285 (kNm) M z = 150 (kNm) 8. CONCLUSIONS The algorithm of calculations of the total moments (i.e. slenderness effects) in non-sway/sway column has been presented. The results obtained with the program (see point 6 – Results of the Section Calculations) are in agreement with the manual calculations (see point 7.3 – Final Result). LITERATURE [1] B.A.E.L. 91. Règles techniques de conception et de calcul des ouvrages et constructions en béton armé suivant la méthode des états-limites. Mod. 99. [2] J. Perchat, “Pratique du BAEL 91”, Deuxième èdition, Eyrolles, 1998, Example 2, pp. 98 [3] J-P. Mougin, “Béton Armé. BAEL 91 et DTU associés”, Eyrolles, 1995, Example 1, pp. 113 March 2014 page 10 / 10

© Copyright 2020