Determine the force in each of the members located to the right of D E for the inverted Howe roo

Determine the force in each of the members located to the...

Key Concepts

Truss Analysis

Truss analysis is the study of forces in a framework composed of members connected at joints. It involves determining the internal forces in each truss member to ensure the structure remains in equilibrium under applied loads. This analysis is fundamental in structural engineering to guarantee that the design can safely carry the designated loads.

Equilibrium Conditions

Equilibrium conditions refer to the requirement that the sum of all forces and moments acting on a structure must be zero for it to stay static. This concept is essential in structural analysis to solve for unknown forces, ensuring that every joint and member satisfies the conditions of static equilibrium.

Method of Joints

The method of joints is a technique used in truss analysis where each joint is isolated, and the forces acting on it are analyzed. By applying the equilibrium conditions at these joints, the internal forces in the connecting members can be systematically determined.

Method of Sections

The method of sections is an alternative approach in truss analysis that involves cutting through the truss to create a section and then applying equilibrium conditions to that section. This method can provide a more direct way to calculate the forces in particular members of interest.

Tension and Compression

Tension and compression are terms used to describe the type of internal force experienced by a structural member. A member is in tension when it is subjected to forces that pull it apart, while it is in compression when it is subjected to forces that push it together. Identifying these forces is crucial in understanding the behavior and safety of the structure.

Transcript

00:01 Hi everybody so this is the diagram given in the crystal textbook so here all the measurements are given in feet and lp and in point h in point you can you can find a support there you can see that that is a roller support so due to this support because of this support there will be one reaction that is vertical reaction so let's name this vertical reaction as its way as it is in point h let's name it as h way now in point a in point a you can see another supporter and the name of that support is pin support the specialty of pin support is because of this support there will be two reactions there will be one vertical as well as one horizontal so there will be a vertical let's name the vertical reaction as a way and there will be one horizontal also let's name this horizontal reaction as a as these two are in point a let's name according to that so now let's mention the reaction here in the diagram itself this is hy here this is a y and this will be a h so and let's name this angle here this as beta and the anchor here that as theta now we have drawn the free body diagram so to use the method of joins first let's start with the analysis of this free body diagram of this enter truss and then he look for joins connecting matchman to members with unknown internal forces to solve with force equilibrium equations now let's find the angle theta and beta so theta theta will be tan inverse an inverse opposite by adjacent that is the opposite will be 72 adjacent will be 10 .54 plus 12 .5 that is 23 .04 that ankle is 16 .2 60 degree now about beta beta beta will be tan inverse opposite is 6 .72 and the adjacent is 10 .54 so here the angle is we got it as 32 .52 degree now let's resolve along equation of equilibrium summation of moment at a equal to zero gives us minus 5 .76 feet into 800 lb asforce 800 lb so they are not going to help the force yeah minus the next distance 11 .52 into 800 will be the next 8100 will be the next 800 minus to the next force that distance will be 17 .82 sorry 17 .28 so 17 .28 feet into again 800 minus 0 4 feet into 400 plus 23 .04 h .y.

05:15 Equal to 0.

05:16 So from here, the only unknown here is hy.

05:21 So we can write the value of h .w.

05:26 So we will get hy equal to 1 ,600.

05:35 600 lb now let's move to each joint and find for each joints so firstly let's consider joint edge so for joined edge the diagram will look like this if this is joined edge there will be a 400 will be particularly upward upward to downward 400 will be and there will be just opposite to that this is h y and the f g h and f f h now this angle here that is theta we name that angle as theta so now let's calculate the the summation along y equal to zero gives you h .y minus 400 minus f fh sine theta equal to zero.

07:22 So here we just found the value of h way, substitute the value of h in this equation and we can find the value of fh.

07:34 So therefore the fh, the fh will be equal to 4285 .77 lb.

07:55 And the ffh is actually going inward to the point h.

08:01 You can see the h from here.

08:03 So that creates compression...

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