Staircase analysis

A design stair with an unsupported intermediate platform is verified for deflection and vibrational behavior. In addition to determine the loads on the lower and upper attachments, it is crucial to find out if the stair will show dynamic oscillations that may increase loads as well as produce an uncomfortable shaking during climb.

Staircase with floating platform

A design stair with an unsupported intermediate platform is verified for strength and vibrational behavior. In addition to determine the loads on the lower and upper attachments, it is crucial to find out if the stair will show dynamic oscillations that may increase loads as well as produce an uncomfortable exeperience. The stair is supported by steel profiles, and a steel frame to support the landing. It is mounted to the concrete floor at bottom and to the vertical wooden beam between floors at its top.

Simulation set-up

Element model

A solid second-order tetraeder mesh of the steel frame is created by using the mesh tool in FEDEM. The mass is scaled with a factor of 1.3 in order to account for the wood and railings. A Rayleigh damping coefficient of 0.002, commonly used for steel, is applied.

Load

The dynamic simulation is done by applying a load of 500kg at the center of the platform. The stair will start deflecting from its unladed position. The downward deflection is plotted as function of time in order to show magnitude and frequency. In order to account for the mass of a person contributing to vibrations, a point mass of 80kg is added to the load point.

Boundary condition

The deflection of the stair is ideally only dependent of the stiffness of the steel profiles. However, small deflections in the upper and lower support can contribute strongly to the deflections, and the stiffness of the support bears some uncertainty to it. Hence 2 boundary conditions are tested, which are believed to represent the limits, and that the real answer will lie between those limits. The platform will be held by an M10 bolt for sideways vibration, hence the model platform is fixed in this direction.

BC1 – Non-conservative: All DOFs in mountigs fixed

BC2 – Conservative: All DOFs fixed in translation, free in rotations

Results

The figures show the vertical displacement of Triad 3 vs time. The deflection sets out as a load of 500kg that is suddenly felt on the platform. The deflection observed contain the effect of dynamic amplification. The initial vibrations decay as a result of structural damping. The main results are:

BC1: The initial deflections are about 2mm. Counting the vibrations shows a frequency of about 10Hz.

BC2: Initial deflections are about 8mm, and the frequency is about 6 Hz.

Conclusion

Considering the size of the load used here, the deflections are within acceptable limits. The vibrational frequency will lie in the range 6-10 Hz, which is faster than normal walking and one do not need to worry about resonant amplification.

The actual staircase was build and met the requriments, according to what was predicted by this analysis.