# Beams - 2 | RCC & Prestressed Concrete - Civil Engineering (CE) PDF Download

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.

The document Beams - 2 | RCC & Prestressed Concrete - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course RCC & Prestressed Concrete.
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## RCC & Prestressed Concrete

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## FAQs on Beams - 2 - RCC & Prestressed Concrete - Civil Engineering (CE)

 1. What are the different types of beams used in civil engineering?
Ans. In civil engineering, there are several types of beams used. Some common types include: - Simply supported beams: These beams are supported at both ends and are free to rotate. - Cantilever beams: These beams are fixed at one end and have a free end. - Continuous beams: These beams have more than two supports, which helps distribute the load. - Overhanging beams: These beams have one or both ends extending beyond the supports. - Reinforced concrete beams: These beams are made from concrete and reinforced with steel bars for added strength.
 2. How are beams designed in civil engineering?
 3. What is the purpose of beams in civil engineering?
Ans. Beams play a crucial role in civil engineering structures. Their main purposes include: - Load distribution: Beams help distribute the load from the structure above to the supports, such as columns or walls. - Structural stability: Beams provide stability to the structure by resisting bending and deflection caused by applied loads. - Spanning gaps: Beams are used to bridge gaps between supports, allowing for larger open spaces in buildings or bridges. - Flexibility: Beams can be designed to have specific shapes and lengths, providing flexibility in architectural design and structural layout. - Reinforcement: In reinforced concrete structures, beams help reinforce the concrete, increasing its load-carrying capacity and preventing cracking.
 4. How can I calculate the maximum load a beam can carry?
Ans. The maximum load a beam can carry depends on various factors, such as its material, dimensions, and support conditions. To calculate the maximum load, you can use the following steps: 1. Determine the properties of the beam, including its material, dimensions (length, width, and depth), and support conditions (simply supported, cantilever, etc.). 2. Calculate the moment of inertia of the beam based on its cross-sectional shape. 3. Use the appropriate beam bending formula, such as Euler-Bernoulli beam theory or Timoshenko beam theory, to calculate the maximum moment the beam can resist. 4. Once you have the maximum moment, you can calculate the maximum load by dividing it by the distance between the supports. 5. It is important to consider safety factors and codes/regulations specific to your region or project when determining the maximum load.
 5. What are the common failure modes of beams in civil engineering?
Ans. Beams can fail in different ways depending on the applied loads and structural conditions. Some common failure modes of beams in civil engineering include: - Flexural failure: This occurs when the beam is unable to resist the bending moment and starts to crack or break. - Shear failure: Shear failure happens when the shear forces exceed the beam's capacity, causing it to split or shear along a horizontal plane. - Torsional failure: Torsional failure occurs when the beam twists excessively and exceeds its torsional strength, resulting in cracking or failure. - Buckling failure: Buckling failure happens when the compression forces on a beam exceed its critical buckling load, causing it to buckle or collapse. - Fatigue failure: Fatigue failure occurs when a beam is subjected to repeated loading and unloading cycles over time, leading to cracks and failure. It is crucial to design beams considering these failure modes and apply appropriate safety factors to ensure structural integrity and prevent failures.

## RCC & Prestressed Concrete

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