SSC JE Civil Engineering 23-Mar-2021 Shift 1 Paper

Question : 109 of 200

Marks: +1, -0

Select the correct statement with respect to an over-reinforced cement concrete section under the working stress method.

The allowable limiting stress is reached in concrete before the steel stress reaches the limiting value
The tensile stress in steel reaches the allowable limit before the maximum compressive stress in concrete reaches the allowable limit
Tensile steel stress and maximum compressive stress in concrete simultaneously reach their allowable limits.
The compressive stress in steel reaches the allowable limit before the maximum tensile stress in concrete reaches the allowable limit

Validate

Solution:

Concept:
Working Stress Design Method:
It is a method used for the reinforced concrete design where concrete is assumed as elastic, steel and concrete act together elastically where the relationship between loads and stresses is linear.
The analytical aspect of the design of reinforced concrete beams:

(a) From stress Diagrams

{\f_{\cbc}}/{\kd}={\f_{\c \t}}/{(\d-\k \d)}

\f_{\c \t}={\f_{\c \b\ c}}/{\k}(1-\k)

(b) From Strain Diagram

{{\f}_{{\st}}}/{{\E}_{{\st}}}={{\f}_{{\ct}}}/{{\E}_{{\c}}}

\f_{\c \t}={\E_{\c}}/{\E_{\s \t}} \f_{\s \t}={\f_{\s \t}}/{\m}

{\f}_{{\st}}={\mf}_{{\ct}}

where

{\m=280}/{3 \σ{\c \b \c}}

(c) From Force Equilibrium
C - T = 0
or C = T
or

1 / 2 {\f}_{{\cbc}} {\bkd}={\f}_{{\st}} {\A}_{{\st}}

(d) From Moment Equilibrium
Applied Bending Moment = Resisting Bending Moment
or

{\M}_{{\applied}}={\M}_{{\R}}={\C} 1 {}_{{\a}}={\T} 1 {}_{{\a}}

{\M}_{{\R}}={1}{2} {\f}_{{\cbc}} {\bkd}({\d}-{{\kd}}/{3})={\f}_{{\st}} {\A}_{{\st}}({\d}-{{\kd}}/{3})

{\M}_{{\R}}={1}/{2} {\f}_{{\cbc}} {\kbd}^{2}(1-{{k}}/{3})={\f}_{{\st}} {\A}_{{\st}}(1-{{k}}/{3}) {d}

{\M}_{{\R}}={1}/{2} {\f}_{{\cbc}} {\kbd}^{2} {\j}={\f}_{{\st}} {\A}_{{\st}} {\jd}

{\M}_{{\R}}={\Rbd}^{2}={\f}_{{\st}} {\A}_{{\st}} {\jd}

Where

{\j}=(1-{{\k}}/{3})

and

{\R}={1}/{2} {\f}_{{\cbc}} {\kj}

Based on fundamentals of analysis in the above section, a singly reinforced rectangular section may be put in any of the three categories: (I) A Balanced Section
(ii) An Under-Reinforced Section
(iii) An Over-Reinforced Section
Explanation:
Over-Reinforced Section:

The working stress design of over reinforced RC section:
1 The percentage of steel provided is more than that provided in the balanced section. So the section is uneconomical.
2 The actual neutral axis is below the critical neutral axis.
3 The allowable limiting stress is reached in concrete before the steel stress reaches the limiting value.

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