Determine the zero-force members in the truss of (a) Prob. 6.21 , (b) Prob. 6.27 .

Name: Problem 34, Chapter 6: Vector Mechanics for Engineers: Statics and Dynamics
Uploaded: 2020-09-03T00:43:08-08:00
Duration: 11 min 35 s
Channel: Sajay Krishnan Paruthiyil
Description: Determine the zero-force members in the truss of (a) Prob. 6.21 , (b) Prob. 6.27 .

Determine the zero-force members in the truss of (a) Prob....

Key Concepts

Truss Analysis

Truss analysis involves evaluating the forces within a structure composed of straight, slender members connected at joints. The primary goal is to determine the internal forces (tension or compression) in the members when the truss is subject to external loads, ensuring that the structure maintains its equilibrium. This analysis is fundamental in structural engineering for designing safe and efficient frameworks.

Zero-Force Members

Zero-force members are specific members in a truss that, under certain loading conditions, carry no tension or compression force. They are identified based on the geometry and equilibrium conditions at the joints. Although not carrying load under a particular set of loads, they can be critical in maintaining the stability of the truss when loading conditions change or during construction.

Static Equilibrium

Static equilibrium is the principle that states a structure or a mechanical system remains at rest when the sum of all the forces and the moments acting upon it equals zero. In truss analysis, ensuring static equilibrium at every joint helps in evaluating the force distribution accurately across the various members.

Method of Joints

The method of joints is a technique used in truss analysis where each joint is isolated, and the equilibrium equations (typically, the sum of horizontal and vertical forces) are applied to solve for the unknown forces in the members meeting at that joint. It is an effective approach for identifying zero-force members as well as determining the tensile or compressive nature of the forces in the structure.

Transcript

00:02 So in this question actually it's a symmetry that means the part left to the fg and right to fg symmetry in this question we need to find only the part left to the fg so here in point a there is a pin support so because of this type of support the support the support what is this type there will be one vertical force let's name it as r a y and there will be another horizontal force also let's name it as r a x and let's draw the forces this is vertical this is horizontal london r .a .y.

01:22 R .a .x.

01:24 Now from the equilibrium of the trust, the support reaction in its direction at joined a is zero.

01:31 So, and join c.

01:39 So the equilibrium of trust, the support reaction in its direction.

02:04 Reaction in its direction that is the arrays equal to zero so now at joint c summation along by equal to zero gives you therefore f b c equal to zero that is at joint c the fbc will be equal to 0 because fac is collinear to f .c.

02:55 So fbc is a zero first member, so that is equal to 0.

03:01 And at joint j, the summation along x equal to 0 gives you fij equal to 0.

03:27 That is fi j is equal to zero that means here this is a at point j right yeah at point j you can see h j is corinear to j l so the f i j will be zero force member so that is zero and summation along y gives you fjk also will be equal to 0 like fj is also equal to 0 because fj is is cornyr to fjn that's way fjk is equal to is 0 for some numbers that is equal to 0 joint having two co -linear members, the third member will be a zero force member if no external commands at alum this member.

04:35 And at joint i, at joint i, the summation along y equals you, f of h, i equal to zero, that is at joint i f of h i that is g i and i k is corlinear so f h i equal to zero that is the joints having two corlinear that is two collinear g i and i k the third member h i will be a zero force member if no external components at a lambda member we already found j i is zero so it's i should be definitely will be zero so these are the zero first members and let's go to the next one here in point e in point e there is a build support and due to this kind of support because the support is this type there will be two reactions there will be one vertical let's call it as ey as well as one horizontal reaction.

06:32 Let's call the horizontal reaction as e.

06:36 And in point f there will be one roller support.

06:49 There is one roller support.

06:54 And because of this kind of support, there will be one vertical reaction.

07:12 So what do your reaction? let's call it as fy...

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