Lesson 1,2,3

Lesson 1 In Design of Reinforced Concrete By Ayman Gamal

1. Load oads , and Loa Load d Ca Cases Load types • • • • •

‫حم‬‫ا‬ Dead Loads ‫الدائمة‬ ‫م‬ Live Loads ‫التشغي‬ ‫م‬ ‫احم‬ ‫الر‬ ‫م‬ ‫احم‬ Wind Loads ‫ر‬ ‫ال‬ ‫م‬ ‫احم‬ Earth-Quack Loads ‫ز‬‫ل‬ Lateral Loads ( Pressure , Earth-Pressure ……….)

‫نبية‬‫الج‬ ‫م‬ ‫حم‬‫ا‬ •

Dynamic Loads ( Machines ,…………………….. ,…………………….. ) ‫م‬ ‫حم‬‫ا‬

‫يكية‬‫د‬ ‫الد‬ •

Other Loads

Load Cases Eccs 203 Ultimate Method 2.

According to Egyptian Code

1-

‫له ن‬‫ى ح‬ ‫شأ و‬‫ى الم‬‫ائمة فقط ع‬ ‫م‬ ‫احم‬ ‫و‬ ‫لة و‬‫فى ح‬ U = 1.4*DL  ‫ي‬ً ‫دوث نسب‬‫ال‬ ‫ن‬ In case of Dead Load Only 2U = 1.4*Dl +1.6*LL U = 1.5*( DL + LL)

when L.L < = 0.75 DL When L.L > 0.75 DL

3U = 1.4*DL 1.4*DL + 1.6*( 1.6*( LL + E ) Where E : Lateral Load Load 1

And Not less Than (2 ‫له‬‫ال‬ ‫ع‬ ‫ق‬ ‫ا‬ ‫ج‬ ‫) و‬ U = 1.4*Dl +1.6*LL when L.L < = 0.75 DL U = 1.5*( DL + LL) When L.L > 0.75 DL 4U = 0.8*( 1.4*Dl + 1.6*LL +1.6*W) where W : Wind Load U = 0.8*( 1.4*Dl + 1.6*LL +1.6*S) where S : Earth-Quack Load And wind load , Earth-Quack Not Combined in One load Case

‫م‬ ‫لة‬‫ح‬ ‫القصى ف‬ ‫حم‬‫ب ا‬‫س‬ ‫ و يت‬‫واحد‬ ‫مي‬ ‫لة‬‫ح‬ ‫ف‬ ‫م‬ ‫ت‬  ‫ز‬‫و ال‬ ‫الر‬ ‫حم‬ ‫الدائمة‬ ‫حم‬‫ى ا‬‫ع‬ ‫ز‬‫ال‬ ‫حم‬ ‫نجم‬ ‫خر‬ ‫ر‬ ‫و‬ ‫ر‬ ‫التشغي‬ ‫حم‬ ‫الدائمة و‬ ‫حم‬‫ى ا‬‫ ع‬‫الر‬ ‫د‬ ‫ى‬‫عنصر ع‬ ‫ك‬ ‫ و ذ‬‫التشغي‬ ‫حم‬ ‫ و‬. We use the Max of  U = 0.8*( 1.4*Dl + 1.6*LL +1.6*W) U = 0.8*( 1.4*Dl + 1.6*LL +1.6*S )

3. Strength Reduction Factor

‫ي‬‫د التس‬‫نة و حد‬‫ر‬‫ة ل‬‫و‬‫ض المق‬‫خ‬   We Use Strength Reduction Factor because the variation of  Material properties such as steel and concrete , Differences in Calculations and Numbering .

‫و‬ ‫س‬‫فى ال‬ ‫و نتيجه التقر‬ ‫قص‬‫او ال‬ ‫ل‬ ‫س‬‫الم‬ ‫ع‬ ‫ا‬‫ة الم‬‫و‬‫ق‬ ‫اخت‬ ‫سب‬ ‫د‬‫ست‬ ‫و‬ ‫فى الم‬ ‫رو‬‫ال‬ γc and γs and

Concrete Reduction Factor γc = 1.5 Steel Reduction Factor γs = 1.15

And In case of Eccentric Compression we Obtain γc , γs From the Equations e / t  ) ≥ 1.5 3 e / t   s = 1.15 (7 / 6 − ) ≥ 1.15 γ   3 c = 1.5(7 / 6 − γ  

2

4. Ultimate Design Concepts

Strain in concrete 0.003 in Flexure that makes apart of section under tension force 0.002 in Compression force acts on the c.g of the section 3

‫فى الشك‬ ‫م‬ ‫فىء‬‫ك‬ ‫ي‬‫مست‬ ‫نه‬‫ر‬‫غط فى ال‬‫ال‬ ‫ي‬‫م‬ ‫ت‬ ‫و‬ , ‫ي‬ ‫نة فى الشد‬‫ر‬‫ة ال‬‫و‬‫ق‬ ‫م‬‫ا‬ ‫ت‬  ‫ى‬‫ع‬ ‫تمد‬ ‫الم‬ ‫مي‬ ‫لى و‬ ‫تر‬ ‫لك‬  3 ‫ ا‬0.003 ‫نه ع‬‫ر‬‫فى ال‬ ‫ن‬‫ا‬  ‫سم‬  ‫و‬ ‫ة‬‫و‬‫س‬ ‫نة‬‫ر‬‫غط فى ال‬‫ال‬  ‫ائم‬ ‫ك‬ ‫ت‬ ‫الق‬ ‫ا‬ ‫م‬ ‫و‬ , ‫القيمة‬ ‫ذ‬ ‫ع‬ ‫ن‬‫ا‬ ‫ ز‬‫عد‬ ‫د‬‫د‬‫الشد فى ال‬ ‫ لق‬, ‫ة‬‫خر‬‫ا‬ ‫ع‬‫ط‬‫فى ا‬ ‫ه‬‫ا‬ ‫ا‬ ‫ا‬ - ‫ة‬‫د لمرح‬ ‫ص‬ ‫د ل‬‫د‬‫ال‬ ‫ك‬ ‫غط و‬‫ة ل‬‫و‬‫ق‬ ‫صى‬‫نة الى ا‬‫ر‬‫ال‬ ‫ص‬ ‫و فيه‬ : ‫ضغ‬‫ا‬ ‫ه‬‫ا‬ ‫ه‬‫ص‬  ‫ى‬ ‫نه و‬‫ر‬‫ال‬ ‫ي‬‫ان‬ ‫سب‬ ( ‫ىء‬ ‫ي‬‫ان‬ ) ‫ص‬ ‫ا‬‫ي‬‫ان‬ ‫الق‬ ‫ي‬‫ان‬ ‫فيك‬ ‫ال‬ ‫ي‬‫ن‬‫ا‬  ‫ذا ال‬ ‫ع‬ ‫ي‬ ‫و‬ ‫م‬ ‫د‬‫الب‬ ‫ج‬ ‫و‬ ‫ي‬‫ن‬‫ا‬ ‫ا‬‫ر ان‬‫ذا اخ‬ ‫و‬ ‫رح‬ ‫لى‬‫الت‬ ‫فى الجداو‬ ‫ا‬‫ال‬ ‫ القي‬‫ع‬ ‫ي‬‫د نسبة التس‬ ‫د‬‫ع‬ ‫ي‬‫ن‬‫ذا ا‬ ‫دث‬ ‫و‬ - ‫ص‬ ‫ظة‬‫ال‬ ‫غط و فى ن‬‫ة ل‬‫و‬‫ق‬ ‫صى‬‫نه الى ا‬‫ر‬‫ ال‬ ‫و‬ ‫ت‬ ‫له‬‫ال‬ ‫ذ‬ ‫فى‬ : ‫از‬‫ت‬ ‫ه‬‫ا‬  ‫د‬‫د‬‫نه و ال‬‫ر‬‫فى ال‬ ‫ي‬‫ن‬‫ا‬ ‫ك‬ ‫و‬ ‫ة ال‬‫رح‬ ‫د الى‬‫د‬‫ال‬ - ‫الى‬ ‫د و‬ ‫د‬‫د‬‫ال‬ ‫ا‬ ‫ فى حي‬‫القص‬ ‫ت‬‫و‬‫ق‬ ‫ب‬ ‫نه ل‬‫ر‬‫ال‬ ‫ك‬ ‫له‬‫ال‬ ‫ذ‬ ‫ و فى‬: ‫شد‬‫ا‬ ‫ه‬‫ا‬  ‫حتى‬ ‫أخذ فتر‬ ‫و‬ ‫شر‬ ‫دث‬ ‫ حي‬‫قد‬ ‫له‬ ‫ك‬ ‫ي‬‫ن‬‫ا‬  ‫ذا ال‬ ‫و فى‬ , ‫حد ال‬ ‫نية‬‫ر‬‫ال‬ ‫ع‬‫الق‬ ‫صمي‬ ‫فى‬ ‫ن‬ ‫اف‬  ‫ذا‬ ‫و‬ ‫الق‬ ‫غط‬‫ال‬ ‫ي‬‫ى ان‬‫ع‬ ‫ ا‬‫التصمي‬ ‫ت‬  ‫ حي‬‫از‬‫المت‬ ‫ي‬‫ن‬‫ الشد – ا‬‫ي‬‫ ان‬‫لتي‬‫ل‬ ‫ر‬  ‫لى‬‫و الت‬

5. Reinforcement of Section subjected to Flexure Ultimate Design Method

‫ة الشد فقط‬ ‫ي‬‫س‬ ‫ا‬ ( ‫و‬‫ال‬ ) ‫ء‬‫ن‬‫ة ل‬‫ر‬‫الم‬ ‫ع‬‫الق‬ ‫صمي‬  

Sections With Tension Steel Only

Section subjected to flexure if applied Compression P is less than 0.1 Fcu*Ac  P  ≤ 0.1 Fcu *  Ac

‫ع‬ ‫ة‬‫القيمة الم‬ ‫ع‬ ‫ق‬ ‫الم‬ ‫م‬‫ال‬  ‫ا‬‫ء إ‬‫ن‬‫ل‬ ‫ر‬ ‫تبر الق‬  M  =

 As *  fy a (d  − )  s 2 γ   

Where 4

 As *  fy γ     s 0.67 * (  fcu / γ    c) * b

a= and a/d Not Less than 0.1

‫بر‬‫ا‬ ‫الق‬ ‫ك‬ 0.1 ‫سبة ع‬‫ال‬ ‫ذ‬ ‫لة ز‬‫فى ح‬

‫ز‬‫ال‬   and yct (Moment Arm) Not More Than 0.95d > 0.1 Yct  ≤ 0.95 d  a / d 

Notes

‫له‬‫فى ح‬ ‫ه الق‬‫م‬‫ت‬ ‫صى ع‬‫ ا‬ ‫ا‬ ‫له الق‬ ‫ر‬‫الم‬ ‫ ال‬‫ك‬ ‫د‬‫له ع‬‫ال‬ ‫ذ‬ ‫د‬‫ست‬  ‫از‬‫المت‬ ‫ي‬‫ن‬‫ا‬ ‫ت‬ ‫از‬‫المت‬ ‫ي‬‫ن‬‫لة ا‬‫فى ح‬ ‫ة الق‬‫م‬‫ت‬ ‫صى ع‬‫ا‬  ‫بر‬‫ا‬ ‫ى الق‬‫ر ع‬‫المؤ‬ ‫ال‬  ‫ا‬‫ف‬ ‫غط‬ ‫ي‬‫دث ان‬  ‫نه ختى‬‫ر‬‫ال‬ ‫د‬ ‫غط ل‬‫قة ال‬ ‫د فى‬‫حد‬ ‫و‬  This Case is Used if the Moment Apllied to Section in < Mmax Where M  =  R max*   fcu * b * d 2 / γ    c

‫از‬‫مت‬‫ا‬ ‫ه‬‫ة ا‬ ‫فى‬ ‫ط‬‫ة ا‬‫يتحم‬ ‫اقصى ع‬

Rmax Steel Grade 240/350 280/450 360/520 400/600 450/520



Cmax/d 0.5 0.48 0.44 0.42 0.40

μmax -4

8.56*10 fcu 7.00*10-4 fcu 5.00*10-4 fcu 4.31*10-4 fcu 3.65*10-4 fcu

Rmax 0.214 0.208 0.194 0.187 0.180

Blanced Section Reinforcement

‫ط‬ ‫از‬‫مت‬‫ا‬ ‫ه‬‫ى ا‬‫ع‬ ‫تصم‬‫ا‬ ‫از‬‫المت‬ ‫ي‬‫ن‬‫له ا‬‫فى ح‬ ‫ه الق‬‫م‬‫ت‬ ‫صى ع‬ ‫و‬‫س‬ ‫ر‬‫المؤ‬ ‫ال‬ ‫ك‬  If M applied = Mmax for the section  Then M  =  R max*   fcu * b * d 2 / γ    c

and Rmax is Given in tables and then  As =  µ max* b * d  where μmax is Given in the Tabel in this Case Falure Accures in Concrete and steel Together

5



Compression and Tension Reinforcement ‫از‬‫مت‬‫ا‬ ‫ه‬‫ا‬ ‫ح‬ ‫قصى‬‫ا‬ ‫ا‬ ‫ع‬ ‫ط‬‫ى ا‬‫مؤثر ع‬‫ا‬ ‫ا‬ ‫ة زي‬ ‫فى‬ ‫ة‬‫خر‬‫ا‬ ‫قد‬ ‫ي‬ ‫ضغ‬‫ة ا‬‫نط‬ ‫ديد فى‬ ‫و‬ ‫ يت‬.

Used when Moment applied to section is > Mmax ( Blanced Section )  Then we Use Compression steel   fy M  = ( R max*   fcu * b * d 2 / γ    c) + ( ) As ' ( d  − d ' )  s γ   

Note : Compression steel In all cases of Design Must be not less than 0.1 As Because it is Useful in Long Term Deflection

‫ى المد‬‫ء ع‬‫ن‬‫فى ا‬ ‫عد‬‫مس‬‫ل‬ ‫ل‬ ‫د الشد و‬‫حد‬  0.1 ‫غط ع‬‫حية ال‬‫فى ن‬ ‫ي‬‫التس‬ ‫ق‬ ‫ا‬ ‫ج‬  ‫ال‬ Stirrups Spacing Mustn’t be less than 15φ for Buckling of Bars 

L and T section Reinforcement

M  = 0.67 (  fcu / γ  c) B * tf  * ( d  −

tf   ) 2

Or M 

=(

 As *  fy tf   )( d  − )  s 2 γ   

Where  Tf is flanged thickness B is Effective width of Flange ‫ء‬‫حن‬ ‫ر‬‫م‬‫ا‬ ‫ع‬‫ط‬‫ة ا‬ ‫ة فى‬‫س‬‫ا‬ ‫ح‬‫ا‬  ‫ة‬ ‫فى ا‬ ‫عم‬ ‫ط‬‫ا‬ ‫تس‬ ‫ة‬‫س‬ ‫اق‬

Note μmin = As/b.d = 1.1/fy where fy (n/mm2) 0.25% Normal Mild Steel 0.15% High Grade Steel Lesson 1 End Best Wishes Eng / Ayman Gamal [email protected]

6

Lesson 2 In Design of Reinforced Concrete By Ayman Gamal

Columns Design in Ultimate Method 1st Design Equations for Columns subjected to Axial compression If the section subjected to P (Axial compression force ) and M (Moment single or biaxial ) and the eccentricity is less than 0.05 t ,0.05 b ( Dimension Under Consideration) Where e = Mu / Pu We use these Equation for Designing the Column .

‫ج‬‫ة فى ا‬‫ر‬‫ال‬ ‫ن‬ ‫و‬ ‫م‬‫ال‬  ‫ى‬‫ع‬ ‫را‬‫ؤ‬ ‫ة و ع‬ ‫غط‬  ‫لة و‬‫فى ح‬ ‫ال‬  0.05  ‫غر‬‫ا‬ ‫ال‬ ‫ج‬‫ة فى ا‬‫ر‬‫ال‬ , ‫ر‬‫ال‬  0.05  ‫غر‬‫ا‬ ‫ر‬‫ال‬  ‫ج‬‫فى ا‬ ‫ال‬  0.05 ‫ى‬  ‫ة المسم‬‫ر‬ ‫ال‬ ‫ا‬ ‫ه حي‬‫ المد‬‫الم‬ ‫دا‬‫ت‬‫ا‬ ‫ت‬  ‫عتب‬‫ا‬ ‫عتب‬‫ا‬  ‫د‬‫الب‬  0.05 ‫او‬  20 ‫د‬‫ت‬   ‫ة المسم‬‫ر‬‫ال‬ ey = My/P<0.05t ex = Mx/p <0.05b Where b (width of Column) in the direction of X Where t (Length of Column) in the direction of Y

For tied Columns  Pu

= 0.35  fcu

*  Ac

+ 0.67   fy

*  Asc

where Ac : Area Of Concrete Section. Asc : Area Of Longitude Steel Bars.  This Chart Using Reinforcement Ratio 1% Where Min Reinforcement Ratio is Max of : 0.8% of Ac Calculated ; 0.6% Of Ac Actual

‫ا‬‫اعتم‬ ,  ‫مسم‬‫ا‬  ‫اق‬ ‫و‬‫ية و ع‬‫ح‬  ‫ر‬‫م‬‫ا‬ ‫عمد‬‫ا‬ ‫صم‬ ‫ى‬ ‫جم‬ ‫ح‬‫ا‬  ‫ه‬ ‫مسم‬‫ا‬ ‫ي‬‫ر‬ ‫ى ا‬‫ع‬ For Spiral Columns Pu is the min of :

‫دائرية‬‫ا‬ ‫العمد‬

‫ية‬‫ا‬ ‫الم‬  ‫غر‬‫ا‬  ‫صى حم‬‫ا‬  Pu  Pu  Pu

= 0.35  fcu

*  Ak  + 0.67  fy *  Asc +1.38  fyp * vsp =1.14 (0 .35  fcu *  Ac + 0.67   fy * Asc ) = 0.40  fcu *  Ac + 0.76   fy *  Asc

‫و‬  ‫ي‬ ‫فة‬‫لمس‬ ‫د‬ ‫ونيه‬‫ح‬ ‫ك‬ ‫عمد‬‫ا‬  ‫ذا ال‬ ‫ن‬ ‫حظة ا‬   Where 8

Ak: Area Of the Concrete Core of Section ( Surrounded by the stirrups)

‫نة‬‫الك‬ ‫اخ‬ ‫نى‬‫ر‬‫ال‬ ‫حة الق‬‫س‬  Asc: Longitude steel bars Fy : Yield stress of longitude steel bars Fyp: Yield stress of Spiral stirrups Vsp: Ratio of steel Volume for One Turn of Spiral Stirrups Where Vsp

≥

 Asp Π

*  Dk   p

‫احد‬‫ال‬ ‫فى الدو‬ ‫ي‬‫د التس‬‫نسبة حد‬

where Asp : Area of spiral stirrup section Dk: Area of the Concrete Core inside Stirrups P: Pitch ( Spacing between turns ) 30-80mm Ratio of stirrups Reinforcement  µ   sp

=

0.36 (

  fcu   fyp

)(

 Ac  Ak 

1)

−

;

 µ   sp

=

Vsp  Ak 

‫و بحمدك‬ ‫له‬‫ا‬ ‫ن‬‫ح‬‫س‬ ‫انت‬ ‫ا‬ ‫ا‬  ‫اشهد ا‬ ‫ي‬‫ا‬ ‫غفرك و ا‬‫اس‬  The End Of Lesson 2 Best Wishes Eng / Ayman Gamal [email protected] Y  

Column Design In Detailed View . 9

‫ع‬‫د ا‬ ‫ئية التى‬‫نش‬‫ر ا‬‫ى ال‬ ‫عمد‬‫ا‬ ‫ق‬‫غر ل‬‫د ا‬‫الب‬ ‫خمسة ا‬ ‫غط ع‬‫ال‬  ‫ج‬‫فى ا‬ ‫د‬ ‫او‬ Ratio “ H/b ” More Than 5 General Considerations Dimensioning

t X  

•

‫غر‬‫د ا‬‫الب‬ ‫ع‬ ‫م‬‫بر ل‬‫ا‬ ‫د الق‬ ‫د‬  ‫ي‬‫ست‬  ‫بة‬‫المر‬ ‫ع‬‫الق‬ ‫ل‬ ‫شم‬ ‫و‬ ‫ق‬‫ل‬ ( ‫غر‬‫د ا‬‫الب‬ ) ‫ر‬‫ال‬ ‫خمسة ا‬ ‫ع‬ ‫ج‬‫ا‬ ‫ فى ا‬‫د ال‬  ‫ي‬  ‫نية‬‫ر‬‫ائط ال‬‫ال‬ ‫لم‬ ‫بق‬ ‫صم‬ ‫نية و‬‫ائط خر‬‫ء ح‬‫ع‬‫ا‬ ‫ذ‬ ‫اعتبر‬ ‫و ا‬

 b

Or We consider it (R.c Wall) and Designed As walls Minimum Eccentricity Ex 0.05b Ey 0.05t Or 20mm t  ≤ 5b

•

Braced Unbraced Column  ‫لم‬ ‫م‬‫ى ال‬‫ع‬ ‫ر‬‫المؤ‬ ‫و‬‫ال‬ ‫عتب‬‫خذ فى ا‬‫ا‬  ‫ر‬‫ة الذ‬‫ل‬‫الس‬ ‫م‬‫ ل‬‫بق‬ ‫عمد‬‫ا‬ ‫صم‬ ‫و‬ ‫نبي‬ ‫قيد‬ ‫ير‬ ‫او‬ ‫قيد‬ ‫ن‬ ‫اء‬ ‫ة‬‫ر‬‫ ل‬‫الدني‬ ‫حدو‬ ‫د ع‬  Column is considered braced if :

‫ى‬‫المب‬ ‫ا‬ ‫ك‬ ‫ستمر‬ ‫نية‬‫ائط خر‬‫ح‬ ‫ع‬ ‫عب‬ ‫دعي‬ ‫ر‬ ‫ا‬‫و‬  ‫ا‬‫قيدا ا‬ ‫ى‬‫تبر المب‬  ‫ية‬‫ا‬ ‫فى الشرو‬‫ست‬ ‫ى و‬‫مب‬‫فقى ل‬‫فى المسقط ا‬ ‫تم‬ ‫ز‬ ‫زعة‬ ‫و‬  The Horizontal load is Carried by Another R.c Members such as Shear Walls And Shear Walls Must Satisfy The following 2 Conditions . 1- Satisfy these Equations α  =  Hb

α  =  Hb

 N 

∑ EI 

< 0.6

 N  < 0.2 + 0.1n ∑ EI 

For Buildings consists of 4 Stories Or More For Buildings consists of Less Than 4 Stories

Where n : No Of Stories N : Total Load Acting On all Vertical Members Hb : Total Height of the building Above the Foundation ‫ف‬ ‫ا‬

‫شأ‬‫م‬‫ل‬ ‫ا‬ 10

 EI  : Sum of Flexure Rigidity of the Shear Walls in the direction ∑

under consideration

‫عتب‬‫ا‬  ‫ج‬‫نية فى ا‬‫ر‬‫ائط ال‬‫ء ل‬‫ن‬‫ا‬ ‫ء‬‫س‬ ‫جم‬  2- Shear Walls Must be connected to the Foundations in a way that allow the transmitting of the Horizontal Loads , and Moments completely to the foundation

‫جة‬‫ال‬ ‫و‬‫فقى و ال‬‫ا‬ ‫م‬‫ال‬ ‫نق‬ ‫سم‬ ‫قة‬‫ر‬  ‫ة‬‫تص‬ ‫نية‬‫ر‬‫ائط ال‬‫ال‬ ‫ك‬ ‫ا‬   ‫إلى ا‬ ‫لك‬ .   ‫نبي‬ ‫قيد‬ ‫م‬‫ال‬  ‫ن‬‫حد‬ ‫ك‬ ‫كذا‬ ‫و‬ ‫ر‬‫ا‬ ‫فى ا‬ ‫د‬ ‫ر‬ ‫و‬ ‫ا‬ ‫ف‬ ‫د‬ ‫عمد‬‫ا‬ ‫ك‬ ‫أ‬ ‫ظة يمك‬‫ح‬  ‫منش‬ ‫ى ا‬‫ع‬ ‫شرو‬‫ا‬  ‫ط‬ ‫يت‬

Long – Short Columns 1st  let us define these parameters i = 0.3b Rectangular Sections .‫الذا‬ ‫ر القص‬ ‫نص‬ i = 0.25 D Circular sections λ  Slenderness Ratio & λ  = He/i ‫فة الق‬‫ن‬   He : Buckling Length of column

‫ى‬‫و الس‬ ‫ال‬ ‫ر‬‫ل‬  ‫م‬‫ال‬ ‫بي‬ ‫لة‬‫ى ح‬‫تمد ع‬ ‫ و‬‫م‬‫ل‬ ‫ال‬ ‫نب‬‫ا‬   ‫س‬‫فى ال‬ ‫حق‬ ‫ة‬‫دا‬‫ت‬ ‫م‬‫ل‬ ‫نب‬‫ا‬  ‫قة حس‬‫ر‬ ‫ة‬‫فى البدا‬ Buckling Length Of Column “He” There are 2 methods for Calculating He 1- Equation Method 2- Simple Method ( Using Tabels ) 1st Equation Method for braced Column He is the Smaller of : ‫نبي‬ ‫المقيد‬ ‫عمد‬‫سبة ل‬‫ل‬   He =  Ho [0.7 + 0.05 (α 1 + α 2)] ≤  Ho  He = Ho [0.85 + 0.05α min] ≤ Ho

for Unbraced Column He is the smaller of : ‫ير المقيد‬ ‫عمد‬‫سبة ل‬‫ل‬ 

‫نبي‬   He  He

= Ho [1.0 + 0.15 (α 1 + α 2)] ≥  Ho

= Ho [ 2.0 + 0.3α min] ≥ Ho

Where α1 is the Lower End Condition  ‫ى‬‫الس‬ ‫ر‬‫ل‬ ‫م‬‫ال‬ ‫بي‬ ‫لة‬‫ح‬

‫م‬‫ال‬ 11

α2

is The Upper End Condition  ‫ال‬ ‫ر‬‫ل‬ ‫م‬‫ال‬ ‫بي‬ ‫لة‬‫ح‬

‫م‬‫ال‬ min is the min of  α1 , α2 α ∑  EcIc

α 

And

=

 Lc  EbIb

∑

 Lb

‫الكمرا‬  ‫ء‬‫س‬ ‫جم‬ / ‫م‬‫ال‬  ‫ء‬‫س‬ ‫جم‬  ‫ية‬‫و الس‬ ‫ة‬‫ة ال‬‫د ال‬‫ع‬

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