Generate a moment-curvature curve for a concrete section shown in Figure 14.15 using the Mander model for confined concrete.

Question

Accepted Answer

Axial load in column = 1000 kN (assumed); axial load capacity = 4100 kN
Section properties:
Width = 500 mm, height = 500 mm, clear cover to ties = 40 mm
Concrete properties:

[latex]f_{ck}[/latex] = 30 MPa, [latex]E_{c}[/latex] = 27400 MPa

Reinforcing steel properties:

[latex]f_{y}[/latex] = 415 MPa, [latex]E_{c}[/latex] = 200000 MPa, [latex]f_{u}[/latex] = 550 MPa, [latex] \in_{u}[/latex] = 0.09, [latex] \in _{sh}[/latex] = 0.0105, [latex]E_{sh}[/latex]= 10000 MPa, [latex]f_{yh}[/latex]= 415 MPa, diameter of longitudinal bars [latex]\phi _{L}[/latex] = 25 mm, diameter of stirrups [latex]\phi _{T}[/latex] = 12 mm and stirrup spacing s = 100 mm.
Mander concrete model
Unconfined strain = 0.002; Unconfined stress = 25 MPa (Cylinder); Ultimate strain = 0.02051
Ultimate stress = 25 MPa; Spalling strain = 0.005; Confined stress = 35.7 MPa
If [latex]A_{shx}[/latex] is the total amount of lateral reinforcement in a hoop layer crossing a section perpendicular to y-axis, then the maximum effective confining stress that can be developed in that direction is given by

[latex]f_{lx}^{\prime}=f_{lx}k_{e}[/latex] (14.13a)

[latex]f_{lx}=p_{tx}f_{yh}[/latex] (14.21a)

∴ [latex]f_{lx}^{\prime}=p_{tx}f_{yh}k_{e}[/latex] (14.25)

For the square cross-section considered in this example:
Effective cover to centre line of the tie (hoop) = 40 + 12/2 = 46 mm
Effective cover to centre of longitudinal bars = 40 + 12 + 25/2 = 64.5 mm
s = 100 mm c/c

Distance between two longitudinal bars = (500 − 40 − 12 − 40 − 12 − 25)/3 = 123.7 mm c/c

∴ [latex]w_{i}[/latex] = 123.7 − 25 = 98.7 mm clear

[latex]A_{i}[/latex] = 12 × 98.72 /6 = 19480 mm²

[latex]A_{core}= x_{cl} imes y_{cl}[/latex] = (500 – 46) × (500 – 46) = 206116 mm²

Net area of concrete [latex]A_{cc}=A_{core} - A_{t}[/latex] = 206116 – 12 × 490 = 200236 mm²

[latex]A_{e}=(A_{core}-A_{i})\left\lgroup1-\frac{s-\phi _{T}}{2x_{cl}} ight group \left\lgroup1-\frac{s-\phi _{T}}{2y_{cl}} ight group[/latex]

[latex]A_{e}[/latex] = (206116 – 19480) × (1 – (100 – 12)/(2 × 454)) × (1 – (100 – 12)/(2 × 454)) = 152240 mm

[latex]K_{e}=\frac{A_{e}}{A_{cc}} = 0.76[/latex]

Total area of lateral steel in x-direction = 4 × 113 = 452 mm²

[latex]p_{tx}=\frac{A_{tx}}{sy_{cl}} =\frac{425}{100 imes (500-46)}[/latex]

The effective confining lateral pressure can be computed using Equation (14.25).

[latex]f_{lx}^{\prime}=p_{tx}f_{yh}k_{e}[/latex] = 0.00996 × 415 × 0.76 = 3.14 MPa

The M-f curve is shown in Figure 14.16.
Idealized plastic moment = 591 kNm
Yield curvature = 0.0000109; ultimate curvature = 0.000113

Question 14.2: Generate a moment-curvature curve for a concrete section sho...

Related Answered Questions

Re-do Example 14.5 and locate the performance point using the EC8-Part 1 method. ...

Verified Answer:

Re-do Example 14.6 and locate the performance point using the EC8-Part 1 method. ...

Verified Answer:

A SDOF system has the following data: Mass = 100 kg, Damping = 5%, Yield strength = 175 N Maximum ground acceleration = 0.25 g Locate the performance point using the ground motion of Example 14.4, if the period is 0.3 sec and capacity curve is bi-linear. ...

Verified Answer:

A SDOF system has the following data: Mass = 100 kg, Damping = 5%, Yield strength = 197 N Maximum ground acceleration = 0.25 g. Locate the performance point using the ground motion of Example 14.4, if the period is 1 sec and capacity curve is bi-linear. ...

Verified Answer:

A 10-storey RC building is shown in Figure 14.28. One of its inner frames is subjected to nonlinear static pushover analysis as well as nonlinear time-history analysis under the El Centro earthquake of May 1940. Determine the target displacement and ductility demands in various members. ...

Verified Answer:

Verified Answer:

Verified Answer:

Draw the response spectrum curves of IS:1893 code on hard soil for 2% and 5% damping in ADRS format. ...

Verified Answer:

Generate moment-curvature curve for a reinforced concrete unconfined section is shown in Figure 14.13. ...

Verified Answer: