When designing and analyzing structural components, one critical aspect to consider is how loads are applied. This seemingly straightforward element can significantly influence the stress experienced by a material. The distinction between instantaneous and gradual load application plays a crucial role in determining whether static or dynamic stress analysis is required.
Instantaneous vs. Gradual Load Application
To ensure accurate stress analysis, it’s essential to understand that for this analysis to apply, the load must be applied instantaneously, with an impact velocity of zero. If the load is applied gradually—even if over just a few seconds—the static stress will develop throughout the material in equilibrium during the load application period.
But what exactly does "suddenly applied" mean?
A suddenly applied load refers to a force that is applied abruptly to a structure or material without prior warning or gradual increase. It differs from gradually applied loads, which allow the materials or structures to deform and adapt over time. This sudden application can lead to unique stress distributions and potentially dangerous failure modes if not properly understood and mitigated.
σSudden = 2 W / A
The Stress (σSudden) due to the “Suddenly Applied Load” in the Rod is MOMENTARILY
TWICE the Static Stress in the Rod due to the Weight (W)
When:
H = 0
VImpact = 0
When a load is applied suddenly, the material experiences a stress that is momentarily twice the static stress for the same load under gradual application conditions.
By utilizing the detailed mathematical descriptions, engineers can devise solutions that mitigate the adverse effects of these loads across different applications.
DISCUSSION AND AN EXAMPLE:
For this analysis to apply, the load application must be Instantaneous and the Impact Velocity must be zero.
If the load application is gradual, even if only over a few seconds, the Static Stress will develop in equilibrium throughout the material during the application period!
The term Suddenly Applied requires some definition, “A load is Suddenly Applied when the Load Application Time is Less than Half of the Fundamental Period, P, of the structural element “
Where P = 1/ωn
So, the Load Application Time must be, tApplication < 0.5 / ωn
Consider the example of a cam follower spring, the peak load is developed over the rise of the cam from low dwell to high dwell:
If the Rise occurs over 90o of camshaft rotation, for a camshaft rotating at 6000 rpm, the peak spring load application develops over 2.5 msec.
The speed of sound in steel is ≈ 16,000 ft/sec. In 2.5 msec, the pressure wave would travel about 480”.
If the Natural Frequency of the spring is, ωn > 200 Hz, then the Loading is Suddenly Applied,
σSudden = 2 σStatic
A Good Conservative Design Guideline!
For other rapidly applied loads, a Dynamic Stress Analysis might be in order, especially if the Impact Velocity ≠ 0, And the Dynamic Stress will definitely exceed the Static Stress!
AUTHOR
Henry T. Bober
Subject Matter Expert, Srushty Global Solutions
Henry is a seasoned Mechanical Design Engineer with 40 years at Xerox Corporation, specializing in Product Development, Cost-Effective Design, and Technology Development. He holds degrees from West Virginia University and the University of Rochester and has 35 patents to his name. After retiring, he founded Fast Forward Engineering, consulting for clients like Xerox, Diebold, NCR, and Siemens Medical Products. Now a Subject Matter Expert at Srushty Global Solutions, Henry lives in Fairport, NY, with his wife Leslie and their pets. He enjoys Western-style horse riding, Japanese garden landscaping, woodworking, naval warfare history, and animal welfare advocacy.