This article discusses about allowable bending stress. The term allowable imposes a limit that cannot be crossed. It defines a safety limit which if crossed can lead to failure.
While designing mechanical components, unknown problems are also taken into account due to which a safety factor is introduced. Increasing safety levels also increase the cost of the product so an ideal amount of allowable stress is negotiated while designing.
What is allowable bending stress?
Allowable bending stress is the safest amount of stress that can be applied on the component without fear of failure. This is a very important term used in mechanical and construction industry. Knowing the allowable stresses helps to decide the appropriate material to be used.
Any amount of stress beyond allowable stress limit is a sign of danger for the component. The formula for allowable bending stress is discussed in later sections of this article. This stress is different from maximum bending stress and can be equal or less than maximum bending stress.
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Maximum bending stress
The value of bending stress beyond which the component will surely fail is called as the maximum bending stress. This is the upper limit of stress or the breaking/ fracture point of the material.
This is the end limit of the stress that can be applied on the material. Beyond this limit the component has 100% probability of failure. This stress is greater than allowable bending stress.
Allowable bending stress formula
Allowable stress depends on various factors, considering each and every factor a single term called factor of safety is derived. The factor of safety differentiates the term maximum bending stress and allowable bending stress.
Maximum bending stress is discussed in above section. The formula for allowable bending stress is given below- σallowable = σmax/Fs
If the factor of safety is unity then maximum bending stress is equal to allowable bending stress.
How to calculate allowable bending stress
The allowable bending stress is calculated by using the formula discussed in above section. The pre requisites of calculating allowable bending stress is determining the factor of safety as per the type of application and maximum bending stress.
Allowable bending strength of concrete
Concrete is largely used in construction industry. Nowadays concrete roads are also prevailing at an immense scale. It is very important to know the bending strength of concrete.
The bending strength of different grades of concrete are given below-
- M15-5.0 MPa
- M20-7.0 MPa
- M25-8.5 MPa
- M30-10.0 MPa
- M40-13.0 MPa
- M45-14.5 MPa
- M50-16.0 MPa
Allowable bending strength of aluminium
Aluminium has mechanical advantage over other metals as it is lighter in weight. There are few aluminium grades which can be easily bent, they are-
- Aluminium alloy 3003
- Aluminium Alloy 5052
- Aluminium Alloy 5083
The bending strength of aluminium grade AL6061 is 299 MPa and this value can increase up to 446 MPa for hybrid CSA composites which is about 49% higher version than the base metal AL6061.
Allowable bending strength of plywood
The bending strength of plywood depends on the number of plies, thickness of lies and the arrangement of grains of plies.
For ply in tension, the bending strength is-
- For grain direction parallel to span-20 MPa
- For grain direction normal to span-15MPa
For ply in compression, the bending strength is-
- For grain direction parallel to span-10MPa
- For grain direction normal to span-8MPa
Above data is taken from test conducted on 5 plies having 6mm thickness each.
Allowable bending stress of wood
There are various types of wood available in market. Most commonly used are- Maple, Oak, Pinewood, Redwood.
The allowable bending stresses of above mentioned wood types are given below-
- Maple– 1271-1491 MPa
- Oak-1369-1610 MPa
- Pinewood-1222-1438 MPa
- Redwood-1320-1553 MPa
How to calculate allowable bending stress example
Let us consider the given data for a sample specimen:
The maximum bending stress that the specimen can hold is 100 MPa.
The factor of safety is to be kept around 1.5
Calculate the allowable bending stress.
The allowable stress can be found using the formula discussed in above section.
After substituting the values in the formula, we get allowable bending stress as 66.67 MPa.