Using the method of joints, determine the force in each member of the truss shown. State whether

step 1 This is the diagram given in the question. So there is point, it's given as point A, B, C, D. An

Using the method of joints, determine the force in each...

Key Concepts

Tension and Compression

Tension and compression refer to the types of internal forces experienced by the members in a truss. Tension occurs when forces stretch the members, effectively pulling them apart, while compression involves forces that shorten or push the members together. Recognizing whether a member is in tension or compression is crucial for assessing the structural performance and safety of the truss.

Free-Body Diagrams

Free-body diagrams are graphical representations that isolate a component or joint of a structure and display all the forces acting upon it. These diagrams are essential in truss analysis as they help in setting up the equilibrium equations and visualizing the force distribution, making the process of solving for unknown forces more straightforward.

Static Equilibrium

Static equilibrium is the condition in which a structure remains at rest because the sum of all forces and moments acting on it equals zero. This fundamental principle underlies the analysis of trusses, ensuring that every joint or segment is balanced by counteracting forces, which allows for the systematic determination of unknown forces.

Method of Joints

The method of joints is an analytical technique used in truss analysis where each joint is isolated, and the equilibrium equations for forces in the horizontal and vertical directions are applied. This approach simplifies the process by allowing the forces in each member connected to the joint to be solved step by step.

Transcript

00:02 This is the diagram given in the question.

00:05 So there is point, it's given as point a, b, c, d.

00:12 And the measurements is given feet and keeps.

00:18 10 feet and 10 feet and 5 feet are the distances given.

00:23 And there are two forces, 10 keeps and 10 keeps in c and d points.

00:30 And here we can see in the joint b the point b there is a roller support so as that is a roller support there will be an external horizontal force let's call it as hb and in point a there is a pin support and we know if there is a pin support there will be an external horizontal as well as vertical force and let's name the vertical force as va and the horizontal force as h a so now let's draw the free body diagram of intertress this looks like the free body diagram of enderatrous so it's a is the horizontal force in point a and hb is the horizontal force in point b and the 10 kids force are given in the question itself and we a is the vertical force in point g .a so let's calculate the equations at equilibrium so for calculating the equations at equilibrium we are to resolve these along y a axis as well as its axis.

02:11 First let's resolve this alone y axis.

02:15 So summation of y equal to 0 gives va minus 10 minus 10.

02:23 That is this va minus this 10 minus this 10 equal to 0.

02:31 So we will get v a equal to 10 gives.

02:37 Now let's let's resolve against h.

02:42 Saxis.

02:44 Resort along hsatis gives us summation of h equal to 0, that is hb into the distance 5 feet equal to the 10 into this distance 10 and plus 10 into the whole distance 20.

03:07 So we will get hb equal to 60 keeps.

03:17 So and likewise we can find the value of ha that is also will be 60 kids.

03:26 So now let's resolve, let's find all the other things by resolving individual joints.

03:37 Let's name this join as a and the other as b and c and d.

03:44 So first, let's draw the draw for the joint b.

03:52 There will be sab, h .t along vertical axis, and sbc, and hb, along horizontal.

04:06 So first, let's all along h axis, that is summation of h equal to 0, sbc.

04:17 This svc will be equal to hp and we know the value of hp as 60 keeps so the sbc will also be 60 keeps and as this force is coming inward to the point joint b so this will be compression let's note the compression as c so as vc will be 60 keeps so as this will be compression and let's resolve along vy atzis there is only one force along yat is sab so sab will be zero there is nothing else in my ayes so sab will be zero now let's draw for join b let's find what will be for the join b there will be a horizontal force scd and the keeps vertical and sac making an anchor called let's call it as alpha and sbc.

05:33 So let's find the value of angle alpha.

05:38 You can find it by using taking the tan of alpha that is adjacent by opposite.

05:47 The adjacent is five opposite is 10 feet so tyn of alpha is 5 feet by 10 feet.

05:54 So we will get alpha equal to 206 .565 degree now let's resolve this along y ages that will use us sac into sine alpha equal to minus the yeah sac into sac into sign of alpha will give us it along y axis so that minus the other thing along y axis is 10 kids so that minus 10 kids is that thing that minus 10 keeps equal to zero so that will give us the value of sac so we can find the value of sac from this alpha we already know as 26 .56565 substitute that value and we will get sac as 22 .3607 that is also keeps so we got the value of sac and here here the sac is going out so that is tension let's indicate it as d and the above sbc is going inward in case of joint b...

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