Bagatti Alessia-1436375 Preliminary design of beams and columns Tall building structures Tongji University A.Y.2014/2015
Bagatti Alessia - 1436375 A.Y. 2014/2015 Preliminary design of beams and columns Tall building structures Tongji University
Assignment of and beams of th时 DATA hi ftoor =5,5 mi hi-xI toor 3,9 m: l=6m:9k=5,5祭-556=33签 qk=2,5→2,5·6=15 PRELIMINARY DESIGN OF THE BEAMS ACCORDING TO THE ITALIAN CODE Beams c=30 mm is the concrete cover; b=300mm is the width of the beam; h=600mmd600-30=570 mm is the height of the beam; first of all,I evaluate the weight of the beam itself according to the designed dimensions: wm=06m-03m:25°=525兴 Then I evaluate the applied load considering the dead load(in which I consider the weight of the beam as well),and the applied live load: F135·w+9)+15·9=1355,25+33)+15·15=731 Where 1.35 and 1.5 are safety coefficient for dead load and live load respectively
DATA ; ; ; ; . PRELIMINARY DESIGN OF THE BEAMS ACCORDING TO THE ITALIAN CODE Beams is the concrete cover; is the width of the beam; is the height of the beam; first of all, I evaluate the weight of the beam itself according to the designed dimensions: Then I evaluate the applied load considering the dead load (in which I consider the weight of the beam as well), and the applied live load: Where 1.35 and 1.5 are safety coefficient for dead load and live load respectively
Ma=20-7315=26325州 10 This value of the applied bending moment is an average value between fixed and hinged end supports. Assuming ductile failure of the cross section: 5-音=0256→Type I fatbre 0,8bxfea(d-0,4x)=Mga 2 Msa I estimate the maximum moment in the position of the tensile steel 1 570mm=d≥ 0,8b1-0,45万 =126,14mm→Verified All the beams will be 30cm x 60cm Columns As far as the Italian Code is concerned,let gk =5.5 kN/m2 and qk=2.5 kN/m2.The concrete that has been used is(for the Italian code)C28/35,for which: a=袋=08s-1587w Ye Where: :Reduction factor that takes into account the resistance reduction due to long-term effects; Y:Reduction coefficient; fe:Concrete design strength. The load combination for dead and live load,using the Euro Codes(Yc=1.35 and Yo=1.5): q=YG19x+Yoqx 11.175 kN/m2 After that,I evaluate the load for the three different column I want to predesign(central column border column,corner column);since the influence area is different,I have: V%x6=Vcentral=11.175*6*6=402.3kW V6x3=Vporder=11.175*6*3=201.15kW V33=omer=11.175*3*3=100.58kW The formula given by the Italian Code is as follows
This value of the applied bending moment is an average value between fixed and hinged end supports. Assuming ductile failure of the cross section: I estimate the maximum moment in the position of the tensile steel. All the beams will be Columns As far as the Italian Code is concerned, let and . The concrete that has been used is (for the Italian code) C28/35, for which: Where: : Reduction factor that takes into account the resistance reduction due to long-term effects; : Reduction coefficient; : Concrete design strength. The load combination for dead and live load, using the Euro Codes ( and ): After that, I evaluate the load for the three different column I want to predesign (central column, border column, corner column); since the influence area is different, I have: The formula given by the Italian Code is as follows:
N Where the design strength of the concrete has been reduced of 50%less,N is the axial force applied to the column,and l.min is the minimum width of the column. Note that also in the Italian Code,the value of N need to be incremented by a factor B,which considers the position of the column in the structure itself(whether the column is central,on the sides or on the corners) Central column:B=1.0; Side column:B 1.1;B =1.2. In the evaluation of the weights,I considered also the parts of beams coming into the columns(i.e. 12 metres of beams for the central column,9 metres for the side columns and 6 metres for the corner columns). Here as follows the weights of the single floors have been computed on the way down,summing up the weights coming from the upper levels: WEIGHTS Floor Central column [kN] Side column [kN] Corner column [kN] 12 456.3 261.765 147.69 11 912.6 523.53 295.38 10 1368,9 785,299 443,0 9 1825.2 1047.06 590.76 22815 1308825 738.45 2737,8 1570,59 886,14 6 3194,1 1832.355 1033.83 3650,4 2094,12 1181,52 4106,7 2355,885 1329,21 4563 2617.65 1476.9 5019,3 2879,415 1624,59 5475.6 3141,18 1772.28 Here as follows are the minimum width of the column cross section,evaluated as written before: WIDTHS Floor Central column [mm] Side column [mm] Corner column [mm] 12 239,8014 181,6278 136.4275 11 339,1304 256,8605 192,9377 415,3483 314,5886 236,2994 9 479,6029 363,2556 272,8551
Where the design strength of the concrete has been reduced of 50% less, N is the axial force applied to the column, and is the minimum width of the column. Note that also in the Italian Code, the value of N need to be incremented by a factor , which considers the position of the column in the structure itself (whether the column is central, on the sides or on the corners): Central column: ; Side column: ; In the evaluation of the weights, I considered also the parts of beams coming into the columns (i.e. 12 metres of beams for the central column, 9 metres for the side columns and 6 metres for the corner columns). Here as follows the weights of the single floors have been computed on the way down, summing up the weights coming from the upper levels: Here as follows are the minimum width of the column cross section, evaluated as written before: WIDTHS Floor Central column [mm] Side column [mm] Corner column [mm] 12 239,8014 181,6278 136,4275 11 339,1304 256,8605 192,9377 10 415,3483 314,5886 236,2994 9 479,6029 363,2556 272,8551 WEIGHTS Floor Central column [kN] Side column [kN] Corner column [kN] 12 456,3 261,765 147,69 11 912,6 523,53 295,38 10 1368,9 785,295 443,07 9 1825,2 1047,06 590,76 8 2281,5 1308,825 738,45 7 2737,8 1570,59 886,14 6 3194,1 1832,355 1033,83 5 3650,4 2094,12 1181,52 4 4106,7 2355,885 1329,21 3 4563 2617,65 1476,9 2 5019,3 2879,415 1624,59 G 5475,6 3141,18 1772,28
5362123 4061321 305,0613 > 587,3911 444,8954 334,1779 6 634,4549 480,542 360,9534 678.2609 513.721 385.8754 4 719,4043 544,8834 409,2826 3 758.3187 574.3575 431.4218 795.3314 602.3913 452.479 G 830,6965 629,1772 472,5989 Starting from the previous table,the width of the column has been evaluated as follows: WIDTHS Central column [mm] Side column [mml Corner column [mm] 12 300 300 300 00 300 10 50 300 500 400 300 600 7 600 500 400 6 700 500 400 54 700 600 400 800 600 400 800 600 500 2 600 500 850 650 500
8 536,2123 406,1321 305,0613 7 587,3911 444,8954 334,1779 6 634,4549 480,542 360,9534 5 678,2609 513,721 385,8754 4 719,4043 544,8834 409,2826 3 758,3187 574,3575 431,4218 2 795,3314 602,3913 452,479 G 830,6965 629,1772 472,5989 Starting from the previous table, the width of the column has been evaluated as follows: WIDTHS Floor Central column [mm] Side column [mm] Corner column [mm] 12 300 300 300 11 400 300 300 10 500 400 300 9 500 400 300 8 600 400 300 7 600 500 400 6 700 500 400 5 700 600 400 4 800 600 400 3 800 600 500 2 800 600 500 G 850 650 500