Beams (Part - 2) Civil Engineering (CE) Notes | EduRev

Civil Engineering SSC JE (Technical)

SSC : Beams (Part - 2) Civil Engineering (CE) Notes | EduRev

The document Beams (Part - 2) Civil Engineering (CE) Notes | EduRev is a part of the SSC Course Civil Engineering SSC JE (Technical).
All you need of SSC at this link: SSC

Chapter 2 Beams (Part 2)

 

B. Analysis (a) Singly reinforced rectangular section (i) Actual depth of neutral axis (Xa)

 

Here, B = Width of beam D = Overall depth d = Effective depth

 

s = C = permissible stress in concrete s = t = st permissible stress in steel In working stress method, actual depth neutral axis is calculated by equating moment of area on both sides of neutral sides.
On compression side, Moment of area = 2
X
B.X . a
a On tension side = ( m.A st ) (d – X a ) For actual depth of NA mA (d X ) 2
BX
a
st
2
a
-
=
(ii) Critical depth of Neutral Axis (Xc)

 

Critical depth of neutral axis is that depth at which stresses in concrete and steel are attained to its maximum permissible values at the same time.
From similar triangle

 

 

 

 

k is called critical neutral axis depth factor

 

 

(iii) Moment of resistance: Maximum capacity of taking moment of a given RCC sections is called moment of resistance. 1. For Balanced section (Xa = Xc):

 

Moment of resistance = compressive force x lever arm or total tensile force × lever arm

 

lever arm = distance between C and T

 

Moment of resistance for a balanced section,

 

 

or balanced section Design of Beam For a given BM = M Equating BM = Mr M = Q.B.d2

 

Where, Q = moment of resistance coefficient Area of steel for a balanced section BM = Mr

 

(For balance section)

 

2. For under reinforced section (Xa < Xc)

 

Here,
Xa < Xc Ca < s cbc ta = sst From similar triangle

 

Properties  Steel gets its maximum permissible value first, concrete is under stressed.  Failure of section will be due to steel.  Failure of section is called ductile failure  It provides sufficient time  before failure this type of section is preferred. 3. For over-reinforcement section (Xa > Xc)

 

Properties:  Concrete gets its maximum permissible value first, steel is under stressed.  Failure takes place due to failure of concrete  Failure of concrete is sudden (brittle failure) this type of structure should be avoided. (b) Doubly reinforced section If depth and width are restricted.
If this beam has to support a BM more than Mr of the balanced section.
Ther are 2 options.

 

 Provide an over-reinforced section, or  Provide a doubly Reinforcement-section Over re-inforced section has many disadvantage like brittle failure so always a doubly reinforced section is a better option.
Properties  Steel is provided on both side of NA  Permissible stress for compression steel = 1.5 mC where C' = stress in concrete around compression steel.  Equivalent area of steel in terms of concrete for compression steel = 1.5 mAsc For tension steel equivalent area = mAst. (i) A ct ual Dep t h of N eut r al A xi s, (X a)

 

Equating moment of area on both sides of NA ( )( ) ( a ) st
c sc a
2
a 1.5m – 1 A X d mA d X 2
BX
-
+ - =
Here, Xa = Actual depth of Neutral axis (ii) Critical Depth of Neutral Axis, (Xc) .d t mc m
X c
c
+
=
(iii) Moment of Resistance (Mr)

 

C' can be calcualted using similar triangles For a balanced section Xa= Xc Ca = s cbc

 

 

 

 

Properties
• Steel gets its maximum permissible value first, concrete is under stressed.
• Failure of section will be due to steel.
• Failure of section is called ductile failure
• It provides sufficient time before failure this type of section is preferred.
3. For over-reinforcement section (Xa > Xc)

 

 

Properties:
• Concrete gets its maximum permissible value first, steel is under stressed.
• Failure takes place due to failure of concrete
• Failure of concrete is sudden (brittle failure) this type of structure should be avoided.

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

MCQs

,

Viva Questions

,

ppt

,

Summary

,

Sample Paper

,

Previous Year Questions with Solutions

,

practice quizzes

,

Beams (Part - 2) Civil Engineering (CE) Notes | EduRev

,

Beams (Part - 2) Civil Engineering (CE) Notes | EduRev

,

Exam

,

shortcuts and tricks

,

Objective type Questions

,

Beams (Part - 2) Civil Engineering (CE) Notes | EduRev

,

pdf

,

video lectures

,

study material

,

mock tests for examination

,

Extra Questions

,

Important questions

,

Free

,

Semester Notes

,

past year papers

;