For the given loading, determine the zero-force members in each of the two trusses shown.

Name: Problem 32, Chapter 6: Vector Mechanics for Engineers: Statics and Dynamics
Uploaded: 2020-09-03T00:05:03-08:00
Duration: 10 min 3 s
Channel: Sajay Krishnan Paruthiyil
Description: For the given loading, determine the zero-force members in each of the two trusses shown.

For the given loading, determine the zero-force members in...

Key Concepts

Truss Analysis

Truss analysis involves evaluating a framework of straight members connected at joints to determine the forces acting on each member. This analysis typically assumes that the loads and forces are applied only at the joints, and that the members are only subject to axial tension or compression. It forms the foundation for determining which members are critical for stability and which may not carry any load under certain conditions.

Zero-Force Members

Zero-force members are elements in a truss that, under specific loading conditions, do not carry any tensile or compressive force. Their presence is essential for maintaining the structure's stability under various loading scenarios, making the truss robust against potential reconfigurations of load paths. Identifying them usually involves looking at joints where only a limited number of non-collinear members meet without any external load or support reaction.

Method of Joints

The method of joints is a technique used in truss analysis where the equilibrium of forces (sum of forces in both horizontal and vertical directions equating to zero) is applied to each joint. This method helps to systematically solve for the forces in the truss members and can reveal zero-force members when the balance of forces at a joint indicates that certain members do not contribute to the force equilibrium under the given loading.

Method of Sections

The method of sections involves cutting through a truss to isolate a subset of the structure and applying equilibrium equations to that section. This method allows for the determination of internal forces in specific members, often making it easier to identify members that do not experience any axial force, i.e., zero-force members, under the applied load.

Equilibrium Conditions

Equilibrium conditions dictate that the sum of forces and moments in a static system must equal zero. In the context of truss analysis, ensuring that each joint fulfills the equilibrium criteria helps in identifying which members are active or redundant (zero-force members). Applying these conditions is crucial in ensuring the structural integrity and in determining the internal force distribution among the truss members.

Transcript

00:01 Here sees 6 .32 so there is two truss so in trust a you can see in point l there is a pin support so because of this type of support the support is this type there will be two force one vertical first let's call it as rl as well as one horizontal force let's call it as rlads and in point h there is another type of support that is roller support so because of this type of support there will be one force that is vertical there will be a one vertical force let's call that as rh y now in trust b interest b in point p there is a roller support there because of the support there will be a vertical force so let's call the vertical forces r py and in point j there is a pin support there is a pin support so because of this type of support there will be two reactions one vertical as well as a horizontal reaction so there will be one vertical reaction let's call the vertical reaction as r and say y and there will be one horizontal reaction also let's go the horizontal one as r j -h.

03:07 Now let's draw the reactions here itself.

03:18 This will be r -l -y and the results this as r -l -h and here this is r -h -y.

03:28 And here this is r -h -y.

03:35 And here this is r -b -y.

03:40 And here this is r -j -y this one is r -j -x we have drawn the forces reactions everything now to calculate the so zero force member now let's examine the free body diagram of the intertress and search for the zero force member we you know zero force member is dictated when we have a three member in the same joint and two of them are coaling that is in a straight line so that third are zero force one so first let's start with joint let's start with join with truce a so trust a let's consider first the joint b.

04:59 So in join b, let's bring here.

05:03 Interstate in join b.

05:06 You can see this is going here.

05:08 So the force fbj, the force fbj will be 0.

05:19 And next about joint d.

05:28 In joint d, yeah in here in join d.

05:36 This is linear.

05:38 So that means fdi will be zero...