August 11, 2021

January 19, 2022

- Building Construction (74)
- Building Materials (70)
- Columns (2)
- Concrete Beam (3)
- Concrete Construction Techniques (4)
- Concrete Mix Design (9)
- Concrete Repair (11)
- Concrete Slab (10)
- Construction Equipment (14)
- Construction News (7)
- Design of Structures (14)
- Engineering Drawing (1)
- Estimation (2)
- Geotechnical engineering (24)
- Highway Engineering (11)
- Innovations (26)
- Material Testing (8)
- Matrix Analysis of Structures (2)
- Mechanical Engineering (3)
- Transportation Engineering (9)

Neenu
February 16, 2020

A bar suspended freely from a fixed end is subjected to an elongation dlÂ which is caused by its own weight. Here, the value of elongation of a freely suspended bar is determined.

###
Â Elongation of a Bar by its Self Weight

####
Step 1: Weight of the bar of the length 'x'Â

####
Step 2: Stress on the element 'dx'

####
Step 3: Strain in the element 'dx'

####
Step 4: Elongation of the Element

####
Step 5: Elongation of the Bar

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â dl****= WL/2E**

Elongation of a Bar by its Self Weight |

Consider a bar AB that is freely suspended, with one end fixed. The length of the bar be 'L', area of cross-section be 'A', 'E' be the modulus of elasticity and 'w' is the weight per unit volume of the bar material.

Consider a small strip of thickness'dx' at a distance 'x' from the free end 'B'.

Let the weight of the bar of length 'x' be P. Then,

P = Specific weight x Volume = Specific weight x area x thickness = w . A.x

This implies, on the strip of length 'x' a weight is acting downwards whose value is P = wAx.

The stress on the element 'dx' is given byÂ = Weight acting on the element / Area of Cross-section

i.e Stress = wAx/A = wx;

This means that, the stress developed due to self weight of the bar is not uniform. It varies with the value of 'x'.Â

Strain in the element = Stress/E = wx/E

Elongation of the element = Strain x length of element = ( wx .dx ) E

The elongation of the bar is obtained by integrating the above equation from 0 to L, and we get

March 02, 2022

January 19, 2022

July 17, 2021

July 02, 2020

March 22, 2024

August 08, 2021

August 11, 2021

September 10, 2017

March 02, 2022

Created By SoraTemplates | Distributed By Gooyaabi Templates

Close Menu

## 1 Comments

Beautifully explained

ReplyDeleteCommenting Spam Links Are Against Policies