+ shape column

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SPARK ’06 A PAPER ON NEW CONSTRUCTION TECHNIQUES “DESIGN OF A PLUS SHAPED COLUMN USING INTERACTION CHARTS” Submitted by Mr. Mayuresh Paradkar Email : [email protected] Phone : 2226575 (Final year Civil Engineering) Guided by: Prof.U.P.Waghe DEPARTMENT OF CIVIL ENGINEERING YESHWANTRAO CHAVAN COLLEGE OF ENGINEERING WANADONGRI, NAGPUR

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Page 1: + shape column

SPARK ’06

A PAPER ON

NEW CONSTRUCTION TECHNIQUES

“DESIGN OF A PLUS SHAPED COLUMN USING INTERACTION CHARTS”

Submitted by

Mr. Mayuresh ParadkarEmail: [email protected]

Phone: 2226575

(Final year Civil Engineering)

Guided by:

Prof.U.P.Waghe

DEPARTMENT OF CIVIL ENGINEERING

YESHWANTRAO CHAVAN COLLEGE OF ENGINEERINGWANADONGRI, NAGPUR

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ABSTRACT

This paper is based on our final year project i.e. design of plus shaped column using interaction curves. The choice of shape of column is depends upon on various factors such as the loading condition, adequacy for space, types of forces, architectural requirements etc.

But it has been often found that to make the column safe larger dimensions than actually required are provided to account for all the loading conditions. But the fact is that if we properly adjust the c/s of the column according to the requirement and make use of interaction charts then much economy can be achieved.

In this, we are focusing on the design of plus shaped column. Why this plus shaped column is better than other shaped columns has been explained in the subsequent pages & also what are interaction charts and Purpose of interaction charts is explained.

Basically, the interaction charts which are provided in SP-16 contain only two shapes i.e. rectangular and circular. Our aim to provide the interaction charts for the plus shaped columns so that by using this interaction charts design could be done easily and higher economy can be achieved.

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“WHY PLUS SHAPED COLUMN?”

To check the adequacy of a plus shaped column lets take a square shaped column having c/s area of say 0.36 sq.mt. Therefore, the dimensions of the column will be .6m x .6m i.e. 600mm x 600mm

Now the moment of inertia of this section is Ixx = Iyy= (600^4) /12

= 1.08 x 10^4 mm^4

Now the above section is modified without changing the area

The moment of inertia of the plus section is

Ixx = Iyy = 1.72 x 10^4 mm^4

Thus, (MI) square > (MI) plus

MODIFIED SQUARE SECTION

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Now, the above example clearly shows that plus shaped column is certainly better than square section form the strength point of view.

Moreover if we want the same MI as obtained from the square section, the section of plus column will get reduced contributing to the economy.

The following statistics shows economy that could be achieved by using plus shaped column.

SQUARE SECTION PLUS SECTIONSECTION: SECTION:

AREA = 360 x 10^3 mm.sq. AREA = 300 x 10^3 mm.sq.Therefore,

>> area has reducedMOMENT OF INERTIA:

Ixx = Iyy= (600^4) /12 = 1.08 x 10^4 mm^4

MOMENT OF INERTIA:Ixx = Iyy = 1.72 x 10^4 mm^4

Therefore,>> MI has increased

RATE ANALYSIS:

Assuming depth as 4.5 mt

Therefore, volume=0.36 x 4.5 =1.62 cu mt

Assuming 1% steel = 0.01 Ag = 0.0036 sq mt volume of steel = 0.0036 x 4.5 = 0.0162 cu mt Wt of steel =0.0162 x 7850 = 127.17 Kg

Assuming 1:2:4 mix,Q= 1.62 cu mt -Adding 15 % for wastageTherefore, Q=1.863 cu mt

RATE ANALYSIS:

Assuming depth as 4.5 mt

Therefore, volume=0.30 x 4.5 =1.35 cu mt

Assuming 1% steel = 0.01 Ag = 0.003 sq mt volume of steel = 0.003 x 4.5 = 0.0135 cu mt Wt of steel =0.0135 x 7850 = 105.98 Kg

Assuming 1:2:4 mix,Q= 1.35 cu mt -Adding 15 % for wastageTherefore, Q=1.55 cu mt

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-Adding 1/3 for dry volumetherefore, Q= 2.484 cu mt

Now , 1 part= 2.484/7 = 0.3549 cu mtMaterial Unit Quantity Rate AmountCement Bags 10.23 173 1769.79Sand Cu

mt0.7094 423 300.07

Aggr. Cu mt

1.4188 565 801.62

Total= 2871.48/-

-Adding 1/3 for dry volumetherefore, Q= 2.07 cu mt

Now , 1 part= 2.07/7 = 0.29 cu mtMaterial Unit Quantity Rate AmountCement Bags 8.5 173 1470.5Sand Cu

mt0.58 423 245.34

Aggr. Cu mt

1.16 565 655.4

Total= 2371.24/->>Nearly Rs. 500 saved on each plus column.

The above statistics shows that the plus column is much economical than the other sections.

ADVANTAGES OF PLUS SHAPED COLUMNS:

1) Now, according to the theory of bending stresses,

f = (M*y)/ INow, as the MI is increasing, the stresses induced will be less and the load

carrying capacity and the moment carrying capacity will increase.

2) Moreover, if we want to design the column for the same designed load and moment as required for the square section, then the dimensions of the plus shaped column will reduce i.e. the amount of material required will be less and economy is achieved .

3) Flexural stiffness (EI / L): It is the moment required for unit rotation.

Here, E= modulus of elasticity of the material.Therefore, the flexural stiffness in case of plus section is greater

than the flexural stiffness for square section.

4) It is many a times required that varying sections of the columns are required at different floors for which complex arrangements are to be done .But in case of plus shaped column, it can be easily done as

Easily shown in the figure below as per the requirement.

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Fig. Applicability of plus shaped column for varying cross sections

INTERACTION CHARTS FOR PLUS COLUMNS:Now, as long as the columns are subjected to concentric axial loads,

the analysis is much simple but the real problem starts when the column is subjected to combined axial load with uniaxial moment or biaxial moment. The analysis in this case is much tedious and involves determination of correct position of NA which requires several trials involving lengthy calculations. Therefore, a simplified approach has been evolved with the help of load Vs moment interaction curve as shown in the figure. It is obtained by plotting various combination of axial force & moment capacity of section determined for different positions of neutral axis.

It provides additional information about compression, tensile and balanced failure points as shown in the figure.

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Now, in SP- 16 the charts are available only for circular & rectangular section. Hence using the above concept we are going to design the interaction charts for plus shaped column so that it can be directly used for any dimension of plus shape, loading condition & grade of steel.

ANALYSIS OF A PLUS SHAPED COLUMN:

In the analysis, different positions of Neutral Axis are considered and for each case the axial load Pu & moment Mu is calculated. Using these values the two ordinates i.e. (Pu / FckbD) & (Mu / FckbD*D) are calculated for different positions of NA to obtain the curve.

ANALYSIS:

CASE 1: Neutral Axis with zero eccentricity:

The ultimate concentric capacity is determined as follows:Pu = 0.446 fck Ac + 0.87fy Asc ………for mild steel.Pu = 0.446 fck Ac + 0.75fy Asc ………for HYSD bars. &Mu = 0 (because, eccentricity=0)Where, Ac = Area of concrete

Asc = Area of steelCASE 2: Neutral Axis with minimum eccentricity emin > 0.05D; emin = D/20:

Pu = 0.4 fck Ag + (0.77 fy – 0.4 fck) Asc.Mu= Pu. Emin

CASE 3: Neutral Axis lying outside the section:

Now,

Pu = cus1+cus2+cus3+cus4+cuc

Cus= compressive force in steel at respective level. = fsc*Area of steel at that leveles= strain at the level of reinforcementCuc= compressive force in concrete. =(0.36 fck.xu.bw – (Area of shaded portion) x width)+0.446 fck(bf - bw).

Mu = cuc((D/2)-0.42xu) + cus1((D/2)-d)+ cus2((D/2) – d) – cus4((D/2) – d) – cus3((D/2) – d).

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CASE 4: Neutral Axis lying at the bottom of the section:

Therefore,

Pu = cus1+cus2+cus3+cus4+cuc

Cus= compressive force in steel at respective level. = fsc*Area of steel at that leveles= strain at the level of reinforcement

Cuc= compressive force in concrete. =(0.36 fck.xu.bw +0.446 fck(bf - bw))

Mu = cuc((D/2)-0.42xu) + cus1((D/2)-d)+ cus2((D/2) – d) – cus3((D/2) – d) – Cus4 ((D/2) – d).

CASE 5: Neutral Axis lying within the section:

Bifurcation of case 5:

ASSUMPTION A) N A lying within web portion as shown:

Therefore,

Pu = cus1+cuc- tu2 – tu3 – tu4Tu= tensile force in steel.

Cus= compressive force in steel at respective level. = fsc*Area of steel at that level

Cuc= compressive force in concrete. = (0.36 fck.xu.bw )

Mu = cuc((D/2)-0.42xu) + cus1((D/2)-d)+ tu2((D/2) – d) + tu3((D/2) – d) + tu4 ((D/2) – d).

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ASSUMPTION B) N A lying within flange portion as shown:

Therefore,

Pu = cus1+cuc+cu2 – tu3 – tu4

Cus= compressive force in steel at respective level. = fsc*Area os steel at that levelCuc= compressive force in concrete. =(0.36 fck.xu.bw ) + 2((Area of portion ii )x (width of portion ii))Mu = cuc((D/2)-0.42xu) + cus1((D/2)-d)+ cus2((D/2) – d) + tu3((D/2) – d) + tu4 ((D/2) – d).

ASSUMPTION C) N A lying below flange portion as shown:

Therefore,

Pu = cus1+cuc+cu2 +cus3 – tu4

Cus= compressive force in steel at respective level. = fsc*Area os steel at that level

Cuc= compressive force in concrete. =(0.36 fck.xu.bw ) + 2((Area of portion ii )x (width of portion ii))

Mu = cuc((D/2)-0.42xu) + cus1((D/2)-d)+ cus2((D/2) – d) + cus3((D/2) – d) + Cus4 ((D/2) – d).

CASE 6: case of pure flexure:

It is the case of pure bending i.e. Pu = 0.

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From all the above cases, Axial load Pu & moment Mu is calculated & the corresponding values of (Pu/(fck(bwd1+bfd2)) & (Mu/fck(bwd1*d1+bfd2*d2)) is calculated and these values are plotted on X & Y axis respectively to obtain the curve.

Now again some another % of steel is assumed & again the same procedure is repeated so that the curves are obtained for p/fck of 0.02, 0.04…., 0.26 for a particular value of (d/D) and grade of steel. Following figure shows the probable model of an interaction chart for a plus shaped column.

(Fig: Showing model of plus shaped interaction chart)

SCOPE OF IMPROVEMENT: In the above paper we have only considered the plus shaped column which could

be very effectly used for the interior columns.In the similar manner if we want to achieve economy for exterior columns too then then the design charts for T shape & L shape could be drawn.

REFERENCES & GUIDELINES:

1) Our Guide: Prof.U.P. Waghe.2) Books: LSM & Design of reinforced concrete by :

a)Dr.Shah & Karveb) Dr. Sinha

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