Question

Q1. The short tied column is to be used to support the following factored load and moment: P= 1250 kN and M= 250 kN.m [10 marks]. fc=28 MPa fy=420 MPa

a) Determine required dimensions and reinforcing bars using appropriate ACI column approach [2 marks].

b) Determine maximum ACI design axial load strength for selected column [2 marks].

c) Determine balanced failure point on axial moment interaction diagram [2 marks].

d) Determine the tie size and spacing [2 marks].

e) Draw the typical tie arrangements dimensions [2 marks].

Answer 1

a)

e)

b)

c)

design of column based on ACI code is done above.

Steel Ratio Assumption

According to ACI Code 10.9.1, 0.01 < ρg < 0.08

Determination of Concrete Gross Area

According to ACI Code 10.3.6.1,

design strength for tied column, ∅Pn,max = 0.80∅ [0.85f′c(Ag–Ast)+fyAst]

Where, ∅ = 0.65 (ACI Code-02)

consider Pu = ∅ Pn

Pu = 0.80 Ag ∅ [0.85 f′c (1-ρg) + ρg fy]

Selection of Column Size

With the Ag as obtained in step 3 select a square (h2 ) or rectangular (b x h) section, such that the side dimensions are integer multiplier

Check for Steel Ratio

Putting the selected Ag , ρg is calculated. If ρg = 0.01 ≈ 0.08; Design is ok

Otherwise change the column dimension and repeat this step.

Calculation of Reinforcement

Total reinforcement, Ast = Ag * ρg

Now choose required bar size satisfying the ACI Code 10.9.2 requirements i.e. minimum number of bars > 4 Nos.

Selection of Ties

Reinforcement for ties should be selected in accordance with ACI Code 7.10.5.1:

• Use ties of # 3 bar for longitudinal bar up to # 10

• Use ties of # 4 bar for longitudinal bar of # 11, 14, 18 and bundled bar

Determination of Vertical Spacing of Tie

According to ACI Code 7.10.5.2 the vertical spacing shall be smallest of:

• 16 db of longitudinal reinforcement

• 48 db of tie bar

• Least dimension of column section

Arrangement of Ties

ACI Code 7.10.5.3 specifies the arrangement of ties: The ties shall be so arranged that every corner and alternate longitudinal bar shall have lateral support provided by the corner of a tie having an included angle of not more than 135°.No bar shall be farther than 6 in. clear on either side from such a laterally supported bar. Where the bars are located around the periphery of a circle, complete circular ties may be used.