# Design of simple Beams and Coloumns

#### Design of Simple Beam

A member carrying loads perpendicular to its axis is defined as a beam.
For a simple floor beam, I-sections are used.
M/I = (sigma) /y
M = (I/y)(sigma)
I/y = Z (section modulus)
Therefore, M = z(sigma)
When beams are loaded, bending stresses are developed at all sections.
The bending stresses developed in beams can be determined by the equation theory of simple bending.
For laterally supported beams, the permissible bending stress in tension as well as in compression should not exceed (sigma)bc or (sigma)bt = 0.66fy
For laterally unsupported beams, the permissible stress in bending compression is calculated by using tables from the the IS code book (IS:800).

#### Load carrying capacity of the Beam

From structural steel tables for the given beam, the section modulus (Zxx) is obtained.
Depending upon whether the beam is laterally restrained or unrestrained; the value of permissible stress in bending compression ((sigma)bc) is calculated.
The moment of resistance of the beam is found out.
MR = Zxx .(sigma)bc
Equating the moment of resistance to the maximum bending moment equation, the total load (w) the beam can carry is calculated.

#### RCC Column

A column forms a very important component of a structure. Columns support beamswhich in turn support walls and slabs. It should be realized that the failure of a column results in the collapse of the structure. The design of a column should therefore receive importance.
Supporting the slabs is the main function of the columns… Such slabs are called Simply Supported Slabs. Simply supported slabs could be either one way slab or a two-way slab. It depends on the dimensions of the slab.
A column is defined as a compression member, the effective length of which exceeds three times the least lateral dimension. Compression members whose lengths do not exceed three times the least lateral dimension, may be made of plain concrete.
In this article, we are going to discuss in detail the basis of classification of columns and different types of reinforcement required for a certain type of column.

• Rectangle
• Square
• Circular
• Polygon

#### 2. Based on slenderness ratio

• Short column, ? ? 12
• Long column, ? > 12

• A column subjected to axial load and unaxial bending
• A column subjected to axial load and biaxial bending

#### 4. Based on pattern of lateral reinforcement

• Tied columns
• Spiral columns

#### Minimum eccentricity

Emin > l/500 + D/30 >20
Where,  l = unsupported length of column in ‘mm’
D = lateral dimensions of column

#### Longitudinal Reinforcement

• Minimum area of cross-section of longitudinal bars must be atleast 0.8% of gross section area of the column.
• Maximum area of cross-section of longitudinal bars must not exceed 6% of the gross cross-section area of the column.
• The bars should not be less than 12mm in diameter.
• Minimum number of longitudinal bars must be four in rectangular column and 6 in circular column.
• Spacing of longitudinal bars measures along the periphery of a column should not exceed 300mm.

#### Transverse reinforcement

• It maybe in the form of lateral ties or spirals.
• The diameter of the lateral ties should not be less than 1/4th of the diameter of the largest longitudinal bar and in no case less than 6mm.
The pitch of lateral ties should not exceed
• Least lateral dimension
• 16 x diameter of longitudinal bars (small)
• 300mm

#### Helical Reinforcement

The diameter of helical bars should not be less than 1/4th the diameter of largest longitudinal and not less than 6mm.
The pitch should not exceed (if helical reinforcement is allowed);
• 75mm
• 1/6th of the core diameter of the column
Pitch should not be less than,
• 25mm
• 3 x diameter of helical bar
Pitch should not exceed (if helical reinforcement is not allowed)
Least lateral dimension
• 16 x diameter of longitudinal bar (smaller)
• 300mm