Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.


Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.

Column Design (Part 6)

From Column Design Part 1 to 5, we talked about the formulas to calculate the critical buckling load. This time we're going to use the excel spreadsheet program to help calculate. Let's use the following design problem as an example.

The machine designer would like to calculate the allowable load for his steel column having rectangular cross section. The column has section 80 mm x 30 mm, and 380 mm long. It's proposed to use AISI 1040 hot-rolled steel. The upper end is pinned and the lower end of the column is inserted into a close-fitting socket and is welded securely as can in the picture.


To calculate the critical load for the column we need to do as following.

Solid rectangular section, 80 mm x 30 mm.
The area moment of inertia, I = 1/12 x 80 x 303 = 180000 mm4  -- The least I (for this case, around X-X axis) is used.
The cross sectional area, A = 80 x 30 = 2400 mm2
Then the radius of gyration, r = (180000/2400)1/2 = 8.66 mm
Since the column is pinned at the upper end and welded at the lower end, then the end fixity is fixed-pinned.
The practical value of constant K = 0.8 is used for this kind of end fixity.
The effective of the column, Le = KL = 0.8 x 380 = 304 mm
The slenderness ratio = Le/rmin = 304/8.66 = 35.1

The material AISI 1040 hot-rolled steel has yield strength (Sy) and modulus of elasticity (E) as follows.
Sy = 290 MPa
E = 207 GPa

Then we can calculate the column constant, Cc = (2p2 x 207x109 / 290x106)1/2 = 118.7

Because the slenderness ratio (35.1) is less than the column constant (118.7), the column is short. The J.B. Johnson formula should be used.

The critical buckling load becomes,\
Pcr = (2400x10-6) x 290x106[1-(290x106x35.12)/(4p2  x 207x109)] = 665571 N

With the safety factor N = 3, the allowable load for this column is
Pallow = Pcr/N = 665571/3 = 221.8 kN

As usual, mechanical design handbook provides free excel program that can help you solve your column design quickly. Please download the file for FREE at the link below.


Please make sure that macro is enabled so that you can run the program. Once the program is launched, (1) select the end fixity (2) enter values of cross section, column material and safety factor (3) Click calculate to see the result.

Download FREE Excel File of Column Design.
password: mechanical-design-handbook.blogspot.com

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