The truss shown consists of six members and is supported by a short link at A, two short links a

The truss shown consists of six members and is supported by...

Key Concepts

Support Reactions

Support reactions are the forces and moments that occur at the points where a structure is supported. Different types of supports, such as pinned supports, roller supports, and ball-and-socket joints, impose different constraints on the structure. Determining these reactions is a crucial first step in the analysis, as they directly influence the load distribution throughout the truss.

Method of Sections

The method of sections is an alternative approach in truss analysis that involves cutting through the truss to create a section. By analyzing the equilibrium of the isolated section, one can solve for the forces in a subset of the truss members with fewer equations, which is especially useful when only a few member forces are required.

Static Equilibrium

Static equilibrium is the state in which a structure remains at rest because the sum of all forces and moments acting upon it is zero. In truss analysis, this principle is applied to ensure that every joint and the overall structure have balanced forces, which is essential for accurately determining the internal forces in the members and the support reactions.

Truss Analysis

Truss analysis involves studying a framework composed of slender members connected at joints. The goal is to determine the force carried by each member due to external loads. This subject is a fundamental part of structural engineering and is used to ensure that the design can withstand service loads, whether in tension or compression.

Method of Joints

The method of joints is a technique used in truss analysis where each joint is isolated and the equilibrium equations are applied. By solving these equations, one can determine the forces in all the members connected to that joint, making it a systematic and direct approach to analyzing the entire truss.

Transcript

00:01 So here you can see in b there is two supports that is this support will cause bx and this support goes this reaction b way and in joint a there is one support and that goes a a reaction along x and here this is a pin support so because of this type of support there will be three reactions along x y and s is an direction now the dress is symmetrical about x y axis so we can solve only for half the trust and the other half will be same now from symmetry from symmetry here we can notice that b s will be equal to d h and b b s and b y will be equal to d y and now let's apply equilibrium equation in this 3d so summation at momentum it's along its direction equal to zero gives you so first okay first let's do along y okay yeah first let's do along y okay so let's do along y so this gives us the 24 feet 24 into this 400 will be plus the 10 feet that is the distance here this distance is 10 feet into a x 10 feet into a x 10 feet into a x will be equal to zero so from here we can write the value of a .h will be equal to 9 6 .0 ld.

02:37 So we got the value of h.

02:40 Now let's resolve l .h.

02:45 This gives us b .h plus d .h minus a .h equal to zero.

03:01 We know the value of h.

03:02 So and from from symmetry from symmetry oops yeah from symmetry the bh is equal to dh so the bh is equal to dh so if we consider only bh 2 bh a is equal to 2 bx so we therefore bh will be equal to a s divided by 2 that is 960 divided by 2 that is 480 lb so bh equal to dh equal to 480 lb yeah now summation along y equal to 0 gives u b y plus d y equal to this 400 lb and we we know from symmetry b y equal to d y equal to 400 so that means b y equal to d y equal to 200 200 lb now we go the reactions now let's so join c join c join c connects member ac b c and d c so here you can see join c connects members as c b c and d c so let's calculate the distances first like a c will be equal to root of 24 square plus the 10 square and feet plus 0 and this value is 26 feet now about bc let's calculate the distance of bc that will be 24 feet square plus zero square plus seven feet square that is equal to 25 feet now about cd let's calculate the distance of cd that will be 24 feet square plus plus 0 feet square plus 7 feet square and this is equal to 25 feet and now let's calculate the forces we go the distances let's start with fac so fac will be equal to actually the vector fac the vector fac will be equal to the magnitude of facc, ac by ac.

07:14 So facc and we calculated the value of ac, that is 20 seats, 206 multiplied by 24i plus 10j.

07:35 So and fcb, the vector fcb, let's do the calculation here itself...

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