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
fcbc
kd
=
fct
(d−kd)
fct=
fcbc
k
(1−k) (b) From Strain Diagram
fst
Est
=
fct
Ec
fct=
Ec
Est
fst=
fst
m
fst=mfct where
m=280
3σcbc
(c) From Force Equilibrium C - T = 0 or C = T or
1
2
fcbcbkd=fstAst (d) From Moment Equilibrium Applied Bending Moment = Resisting Bending Moment or Mapplied=MR=C1a=T1a MR=12fcbcbkd(d−
kd
3
)=fstAst(d−
kd
3
)MR=
1
2
fcbckbd2(1−
k
3
)=fstAst(1−
k
3
)d MR=
1
2
fcbckbd2j=fstAstjd MR=Rbd2=fstAstjd Where j=(1−
k
3
) and R=
1
2
fcbckj 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.