Special cases

1. If h =0, i.e. a suddenly applied load takes place, we get from the formulas (10.12) and (10.13). Under a suddenly applied load the deformations and the stresses are twice as much than under the statically action of the same load.

2. If the height h of the fall is much more the statically deformation to determine the dynamic coefficient we get the following approximate formula:

(10.15)

 

Example. The load G=1kN from the height h =10 cm =0, 1 m falls on the middle of the steel double - T profile №27 a by the span 3 m. The second moment of the section is the section modulus is (from the tables of the profiles),

Determine the maximum beam deflection and the maximum stresses for its cross section.

Solving. Calculate the statical beam deflection under the load

 

(10.16)

 

The dynamic coefficient is

(10.17)

 

In the given case the dynamic effect of the falling load surpasses its statical effect in 64 times.

Calculate the statically stress from load G. The maximum bending moment will be at the middle beam section:

 

The maximum statically stress is

 

The maximum dynamic stress is

 

 

It can be seen from this example how the dynamic loads are dangerous by their action. Therefore the allowable working stresses under the impact are accepted less than under the action of the statically loads.