Question

the reinforced concrete tied column that is part of braced frame sized to the dimensions 375mm by 300mm .the column carries vertical ultimate load Pu=490kN (dead load only PD=134kN) and ultimate moment about strong axis Mu=110kN at top and Mu=117kN at bottom bent column in single curvature. if the clear height of the column Lu=4.80m k=0.83f'c=28MPa and fy=420 MPa , determine the reinforcement required

Answer 1

Solution:- the values given in the question are as follows:

size of column=375 mm * 300 mm

vertical ultimate load(Pu)=490 KN, (dead load=134 KN)

moment about strong axis(Mut) at top=110 KN

moment about strong axis(Mub) at bottom=117 KN

clear height of column(L)=4.8 m

effective length(Leff)=K*L=0.8*4.8=3.84 m (where, k=0.8)

fIc=28 MPa & fy=420 MPa

Calculation reinforcement required in column:

using limit state(LSM) of method

assume short column with small eccentricity loaded column (e=very less eccentricity 0.05*dimension of column)

ultimate load(Pu)=0.4fIc*Ac+0.75As*fy [Eq-1]

where, Ac=conrete area

As=steel area(reinforcement area)

Ac=gross area-As (gross area=cross-sectional area of column)

Ac=300*375-As

Ac=112500-As mm^2

values put in equation-1

490*10^3=0.4*28*(112500-As)+0.75*As*420 [where, Pu=490*10^3 N ,fy=420 N/mm^2 and fIc=28 N/mm^2 ]

490*10^3=126*10^4-11.2As+315As

490*10^3=126*10^4+303.8As

303.8As=490*10^3-126*10^4=-770000

As=-770000/303.8=-2534.56 mm^2 [area of inforcement not in negative, so negative value taken as positive value]

As=2534.56 mm^2

check the area of reinforcement

minumum area of reinforcement in column according to ACI

Asmin=0.8%of total cross-section area of column

Asmin=(0.8/100)*300*375=900 mm^2

As>Asmin [so the design reinforcement is safe]

let provide 20 mm diameter main bar

number of bar(n)= As/cross-section area of one bar =2534.56/{(3.14/4)*20^2}

number of bar(n)=8.07=8 bars

number of bars(n)=8

ties(stirrups bar)

minimum dia of ties=(3/8)*20=7.5 mm

provide dia of lateral ties=8 mm

spacing of lateral ties=MInimum of{leat lateral dimension of column, 16*dia of main bar, 300 mm}

spacing of lateral ties=MInimum of{300mm , 16*20=320 mm , 300 mm}

spacing of lateral ties= 300 mm

[Ans]