【構造力学】#23 単純梁に等変分布荷重がかかったときの応力図の描き方を徹底解説！

This channel provides easy-to-understand explanations of structural mechanics, physics, and architectural structural design. Recommended for those studying architecture or science and mathematics. This video clearly explains how to calculate stress diagrams when a uniformly distributed load is applied to a simple beam. [Structural Mechanics] #17 A thorough explanation of how to draw N, Q, and M diagrams!    • 【構造力学】#17 N図Q図M図の描き方を徹底解説！   Uniformly distributed load on a simple beam!? Master how to draw shear force diagrams (Q diagrams) and bending moment diagrams (M diagrams)! https://kentikukozosekkei.com/archive... [Quoted from the Online Architecture School] Let's start with diagram Q. Do you remember how to do it? We'll look at the problem from left to right. For detailed instructions, see the article below. Let's start from left to right. Let's focus on point A. The left side of the member is being sheared by an upward force. In this case, is the sign + or -? Check the table below. If the left side of the member is facing upward, the sign is +. The magnitude remains VA, at 3kN. ...So, what do we do from here? At first glance, you probably won't be able to imagine what to do. So, let's memorize the method! There are 3 steps. Just remember this! 3 steps to drawing a Q diagram! 1. Find VB on the Q diagram. 2. Find the point where the shear force is 0. 3. Connect the three points with a quadratic curve. Let's consider each step one by one. 1. Find VB on the Q diagram. This is easy. Let's proceed in the same way as with VA from earlier. The right side of the member is being sheared by an upward force. In this case, is the sign + or -? Check the table below. If the right side of the member is facing upward, the sign will be negative. The magnitude will remain VB, at 6kN. 2. Find the point where the shear force is zero. This is the most difficult part. How do we find it? Let me explain it simply. First, look at only the left half of the problem diagram. (Look at the tip half of the triangle.) If the shear force is zero, that means that VA and the uniformly distributed load triangle are equal in size. (When the force applied from above and the force applied from below are equal (balanced), the shear force is 0.) ...This means we need to find the point where the area of ​​the uniformly distributed load triangle is 3. Now we'll get into some slightly more complicated topics (math). The area of ​​this uniformly distributed load triangle can be easily determined once we know the distance x from the base. This is because the height and base of the triangle are proportional. In this case, the height changes from 0 to 3 kN/m when the base is 6 m. In other words, when the base is 3 m, the height is 1.5 kN/m. When the base is 2 m, the height is 1 kN/m. When the base is 1 m, the height is 0.5 kN/m. If the base is x, when the base is x m, the height is 0.5 x kN/m. Now, we can express the area of ​​the triangle using x. Formula for the area of ​​a triangle From (base) x (height) ÷ 2, x x 0.5 x ÷ 2 This is the size of the triangle with the uniformly distributed load in this problem. Now, we can finally get back to our main topic. The question was at what point does the area of ​​this triangle become 3? So we'll plug it into the formula. Now we can use a scientific calculator to calculate to about two decimal places. On the Q diagram, 0 is 3.46m to the right of VA. This is a fairly difficult section. Please take your time to memorize it. 3. Connect three points with a quadratic curve. If you look at the previous article, you'll see why we use a quadratic curve. It's because the equation contains a square. You squared x when we did it just now, right? That's why. (See the previous article for details.) However, quadratic curves are difficult to draw neatly freehand. So, the correct answer is to connect the three points VA, 0, and VB with a curve. Finally, write down the sign and magnitude, and don't forget the distance from the 0 point. How to Draw an M Diagram Now, as for the M diagram, let's first memorize its shape. The M diagram for a uniformly distributed load is a cubic curve. ...cubic curve...don't get discouraged if you don't understand it! When answering questions in this section, the shape is not very important! Draw a slightly elongated quadratic curve and find Mmax to get the correct answer. How to Find the Sign First, check the sign. Check it in the table below. Since it seems to be positive in this case, we can see that it will curve downwards. How to Find Mmax So, where is Mmax? As I said last time, When the Q value is 0, the M value is at its maximum. Remember that. We just found the point where the Q value is 0. It was 3.46m to the right of VA. So, from that point, we'll just look at the diagram on the left. (You can get the answer by looking at the right, but the equation is complicated, so I recommend looking at the tip of the triangle.) All that's left is to find the resultant...