# Working Stress Study Notes for Civil Engineering Exams

By Vishwajeet Sinha|Updated : January 3rd, 2017

### Working Stress Method

Modulur Ratio where, m = Modular ratio

ES = Modulus of elasticity of steel

EC = Modulus of elasticity of concrete

Equivalent Area of Concrete

AC = mAS

Here, AC = Area of concrete

AS = Area of steel

Stress in Concrete where, pC = stress in concrete

pS = stress in steel

Critical Depth of Neutral Axis (XC)  Here, D = Overall depth

d = Efffective depth

σcbc = c = permissible stress in concrete

σst = t = permissible stress in steel

#### Single Reinforced Rectangular Section

Actual depth of Neutral axis (Xa) Special case:

(i) when Xa = Xc for balanced section

(ii) when Xa > Xc for over reinforced section

(iii) when Xa < Xc for under reinforced section

Moment of resistance (Mr)

(i) For balanced section (Xa = XC)  (ii) For under reinforced section (Xa < XC)  (iii) For over-reinforced section (Xa > XC) Section Stress diagram ### Doubly reinforced section

Doubly Reinforced Rectangular Section

Critical depth of Neutral axis, (XC) Actual depth of Neutral axis, (Xa) Here, Xa = Actual depth of Neutral axis Moment of resistance (Mr)  Design Steps Special case:

(i) Balanced section  (ii) Under reinforced section  (iii) Over reinforced section  Singly Reinforced T-Section where, Bf = Effective width of flange

bw = Width of web

d = Effective depth

Effective width of flange

(a) For beam casted monolithic with slab (b) For isolated T-beam l0 = Distance between points of zero moments in the beam

B = Total width of flange

bw = Width of web

Critical depth of Neutral axis (Xc) When Neutral axis is in flange area

(i) Actual depth of Neutral axis  Here, Xa = Actual depth of Neutral axis

(ii) Moment of resistance (Mr) When Neutral axis is in web area (i) For actual depth of neutral axis (ii) Moment of resistance (Mr) Posted by: Member since Jun 2016 GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com