![]() ![]() Using the same hollow tube to represent the complex product, the Section Properties measurement in SOLIDWORKS shows the I-value needed for the hand calculation. Keeping with the use of the minimum cross-sectional area for calculating stress, I will use the one cross-section that had the minimum second moment of inertia of all the cross-sections measured. Going back to my simplification of the product being a hollow tube, I would need a single value for I. I could also use the Section Properties tool in SOLIDWORKS for each section plane, which may save a little time. This step is a bit time consuming, so I may only do this for a small subset of the area cross-sections. I’ll go back to the cross-sections used for measuring area and use the overall shape and size of that cross-section to calculate a value for I. The key with estimating the second moment of inertia is to get back to the scaffolding example. This is neither simple or accurate for a complex product design! I also need to attempt to estimate the second moment of inertia, I. The length of the beam, L, is the overall height of the product, approximately 2.5 meters. I will assume that the entire structure is made with AISI 1020 Steel, which has an Elastic Modulus of 205,000 MPa. I’ll select one material to use here for a value of E, or Young’s Modulus. The actual product is an assembly with a few different materials used in the primary structure. But if I make that assumption, the critical load can be calculated by this formula: I’m going to assume the product will buckle like a simple, pinned beam. ![]() Now I truly must understand the assumptions I’m making for my buckling hand calculation to be “valid”. This is important because the product is subjected to compression loading. The next hand calculation I need is an estimate the critical load that would cause the product to buckle. I’ll reference this as 9.86 MPa per “unit load” of the product. My hand calculation for stress, given the assumptions I’ve made, is this: ![]() For simplicity, I will assume that the multiples of the load are per 10,000 N force. My next assumption is that the loading occurs in multiples of the products stacked height. This is not representative of a stacked product but quantifying the off-axis loading is beyond trying to get a basic understanding of the stress range the product might experience. I also must assume that the loading conditions act along the axis of the tube as a pure compression load. Yes, this is significantly smaller than the actual product, but it will make sense when I get into the Buckling calculations. Let’s assume that I decide to take the smallest cross-sectional area and represent that as a simple shape, like a hollow tube. Or I could estimate the maximum expected stress using the smallest area measured. I could also choose to calculate an average of the load bearing areas for all the cross sections to estimate stress through the entire structure. I can choose to estimate the stress at each cross section since the maximum load (force) is known. There are multiple approaches to a hand calculation for stress at this point of my investigation. I would create several reference planes in the CAD model at a consistent spacing, then measure how much material is at each cross-section, and tabulate the results of those measurements. The load bearing area through any one cross-section parallel to the ground can be easily found using SOLIDWORKS. A visual example of the load bearing area could be a scaffolding. Estimating the load bearing area for this product is quite challenging. That hand calculation for stress is easy – force divided by area. I need two different hand calculations for this, one for stress and one for buckling. Now, I cannot discuss the exact product design, but in general terms the product must support large loads and can be stacked several products high. Admittedly I do have to make assumptions for hand calculations to be valid, but it is within those assumptions that I may have an in to soften his stance. My initial response ignores accuracy but focuses on the magnitude of hand calculation results. While I don’t believe hand calculations are a waste of time, it’s hard to argue against accuracy. Good thing I’m thinking about the long game here! That is a strong and fair argument that I cannot win in mere minutes. Simply put, how can an equation referencing material properties, geometric characteristics, or section properties needed in many structural analysis calculations represent the complex designs he creates today. His belief is that hand calculations are a waste of time, that they are never accurate enough to represent what he designs. Recently, I was discussing the use of hand calculations in conjunction with Finite Element Analysis (FEA) with one of our customers.
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