Download MDSolids Example 6.2

MDSolids Example 6.2
Here’s the procedure for using MDSolids to analyze problems where the dimensions are not integral
ratios. Point D is 1.155 m above the line AC, but AC is 4 m and B is 2m above line AC. Therefore, the
spacing and number of spaces to Point D isn’t compatible with the number of spaces and the spacing for
AC and AB. Setting the horizontal dimensions is easy. Choose horizontal distance of 2 m and horizontal
number of spaces as 2. Setting the vertical distance is not so easy because of the 1.155 dimension.
So here’s the process, it’s iterative. A starting point is found by subtracting 1 from 1.155 to yield 0.155.
We need to choose a spacing, k, and a number of intervals, n, such that k*n = 0.155. By inspection, if k =
0.05 and n = 3, then, k*n = 0.150 and the distance to Point D is 1.150. The error is 1.155-1.150 = .005 or
0.43% which for most purposes is sufficiently accurate. We need to check that we also have an integral
number of spaces to Point B. So, 2.00/.05 = 40 (an integer so ok) and the error is zero.
Let’s pick a spacing that will result in a negative error. If the spacing is k = 0.04, then the number spaces,
n, is 1.155/.04 = 28.9 (rounded to 29) and we get the distance to Point D of 1.160. The error is 1.1551.160 = -0.005, or 0.43%, also. Checking for the spacing to Point B, we have 2.00/.04 = 50 (an integer, so
ok) and the error is zero.
Since we have positive and negative errors of the same magnitude, let’s try a spacing of .045 and the
number of spaces, n, is 1.55/.045 = 25.7 (rounded to 26) and the distance to Point D is 1.17. The error is
1.170-1.155 = 0.015 or 1.5%. Checking for the spacing to Point B, we have 2.00/.045= 44.4 (rounded to
44) and the distance to Point B is 1.98 and the error is 2.00-1.98 = 0.02 or 2%.
Based on the analysis above, we could choose any of the above. Let’s choose the first result and set the
spacing at 0.05 m and the number of spaces at 40.
The MDSolids results are shown below and compared to the example solution.
A more precise approach using the optimization capability, Solver (an Excel Add-in), gives quite accurate
results using a spacing interval of 0.0444and 26 spaces for Point D and 45 spaces for Point B. The Excel
results are shown below.
5.02
4.10
4.10
MDSolids Ex 6.2 Using Excel Solver to Find Spacing Interval and Number of Spaces
Item
Maximum Dimension
2
MDSolids Maximum
Dimension
1.
2.
3.
4.
5.
6.
7.
8.
9.
Target Dimension
1.1547
MDSolids Target
Dimension
Spacing Interval
0.0444292
0.0444292
Number of Spaces
Dimension
45
1.9993121
26
1.1551581
Maximum Dimension
Error
0.00068788
Target Dimension Error
-0.0004581
Sum of Errors
Squared
6.83E-07
Notes:
The maximum dimension is the distance of Point B above the line AC. It is highlighted in yellow and is an input.
The target dimension is the distance of Point D above the line AC = 1.547 m. It is highlighted in yellow and is an input.
The spacing interval is one output to define the MDSolids grid and is highlighted in gray.
The number of spaces is the other output to define the MDSolids grid and is highlighted in gray.
The dimension is the calculated value of spacing interval times number of spaces is an output and is highlighted in gray.
The dimension errors are the differences between the input dimensions and the calculated dimensions and are highlighted in gray.
The sum of the errors squared is the sum of the squares of the dimension errors and are highlighted in gray.
Solver adjusts the values of the spacing interval and the number of spacing cells until the sum of error squares is a minimum subject to certain contraints.
Main constraints:
9a. The spacing intervals for Points B and D must be equal since they are the vertical spacing in MDSolids.
9b. The number of spaces must be integers.
9c. All numbers must be positive.
9d. The number of spaces must be less than or equal to 50 for MDSolids use.