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MPSC AE CE Mains 2018 Official (Paper 1)

Option 2 : area of high tensile tendons

CT 1: Engineering Mathematics

1084

10 Questions
10 Marks
12 Mins

__Concept__:

**Moment of resistance:**

- It is defined as the
**algebraic sum of moments of internal forces about the neutral axis of the section**. - For the safety of the structure/section,
**the externally applied moment should be less than or equal to the moment of resistance of the section**.

We know,

**For prestressed concrete**:

As per IS 1343:2012, cl. D.1.

Moment of resistance of rectangular section is given by -

\(M_u = f_{pb} A_{ps}(d-0.42x_u)\)

Here,

f_{pb} - tensile stress in the tendon at failure

A_{ps}- the area of pre tensioning tendons in the tension zone

d - effective depth to the centroid of the steel area

x_{u} - neutral axis depth.

** Explanation**:

Moment of resistance of rectangular section is given by -

\(M_u = f_{pb} A_{ps}(d-0.42x_u)\)

**The moment of resistance of the section depends upon **-

**Area of tensile reinforcement**- Tensile stress in the tendon at failure
- Depth of the section

__Confusion Points__

**For reinforced concrete:**

As per IS 456:2000, cl. G.1.1.

For singly reinforced concrete section,

Limiting moment of resistance of the rectangular section is given by -

In terms of concrete compressive strength (i.e. f_{ck})

\(M_u = 0.36f_{ck}bx_u(d-0.416x_u)\)

In terms of steel tensile stress (i.e. f_{y})

\(M_u=0.87f_yA_{st}(d-0.416x_u)\)