When designing a steel plate subjected to bending under a uniform load, it must ensure the plate can withstand the applied forces without excessive deflection or failure. The following steps outline how to calculate the required thickness of a steel plate for this purpose.
Step-by-Step Approach to Determining Steel Plate Thickness
Plate Framing Considerations
To simplify the design, consider the plate as a one-way framed structure. Install beams in the longer direction at intervals of =< 0.5 Ly ) (where Ly is the longer dimension of the plate or floor). This arrangement effectively transforms the plate into a simple supported system on two beams.
Design Calculation
For design purposes, consider a unit strip of the plate and perform the following calculations:
Moment of Inertia :
The moment of inertia of the plate is calculated based on its thickness using the formula:
Moment of inertia of 1-meter wide strip in mm4 = 1000* Thickness of the plate in mm^3 /12
Here; b= 1m = 1000mm
Section Modulus :
The section modulus is a geometric property that determines the bending strength of the plate. It is calculated as:
Section modulus of 1-meter wide strip in mm3 = 1000*Thickness of the plate in mm^2/6
Here; b= 1m = 1000mm
Self-Weight of the Steel Plate:
Self weight of steel plate is calculated as follows:
Self weight of steel plate in KN/m2 = Density of Steel in KN/m3 *Thickness of plate in mm/1000
Total Applied Load:
The total applied load on the plate includes both the self-weight of the plate and the maximum applied /external load. The total applied load is given by:
Total Applied load in KN/m2 = Maximum Applied load in KN/m2 +Self weight of steel plate in KN/m2
Maximum Allowable Deflection:
The maximum allowable deflection is typically specified as a fraction of the span length. In this case, use L/100 as specified in the code AISC for steel floors
Maximum allowable deflection in mm = Span length in meter *1000/100
Maximum Allowable Bending Moment per Unit Width:
The maximum allowable bending moment per unit width can be calculated using the allowable bending stress and the section modulus:
Maximum Bending moment per unit width in N-m/m = Allowable bending stress in Mpa * Section modulus of 1-meter wide strip in mm3 /1000
Here; Allowable bending stress = Fy/1.67 (As per the AISC code)
Allowable Uniform Load:
The allowable uniform load is calculated based on the maximum allowable bending moment :
Allowable uniform load in KN/m2 = 8*(Maximum Bending moment per unit width in N-m/m *0.001)/(Span length in meter^2)
Actual Deflection:
The actual deflection of the plate can be calculated using the following formula:
Actual Deflection in mm = 5*Total Applied load *((Span length in meter*1000)^4)/(384*Modulus of Elasticity in Mpa*Moment of inertia of 1 meter wide strip in mm4 )
Design Checks
After performing the calculations, ensure the following conditions are met for the plate thickness to be considered sufficient for the applied uniform loading:
- The total applied load must be less than or equal to the allowable uniform load.
- The actual deflection must be less than or equal to the maximum allowable deflection.
If both conditions are satisfied, the selected plate thickness is sufficient to support the applied loads without excessive deflection or failure. If either condition is violated, the plate thickness must be increased.
Design Example
The below two examples are for further concept clarity;
Example 1
Example 2
Conclusion
In conclusion, designing a steel plate subjected to bending under a uniform load requires satisfying two critical conditions: the total applied load should not exceed the allowable uniform load, and the actual deflection should be within the specified limits. If either of these conditions is not met, the plate thickness must be adjusted accordingly to prevent failure or excessive deflection. The provided design examples further illustrate the application of these principles in real-world scenarios.