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

Name: Problem 31, Chapter 6: Vector Mechanics for Engineers: Statics and Dynamics
Uploaded: 2020-09-02T23:50:41-08:00
Duration: 13 min 15 s
Channel: Sajay Krishnan Paruthiyil
Description: For the given loading, determine the zero-force members in each of the two trusses shown.

step 1 So this is question number 6 .31. So here in in point first, yeah, for a, for the trans a in poi

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

Key Concepts

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.

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.

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 So this is question number 6 .31.

00:06 So here in in point first, yeah, for a, for the trans a in point o, there is a role in support.

00:43 So we know that specialty of support.

00:47 Because of this support there will be a vertical force.

00:53 And let's call it as roy and in point a there is a pinned support we know the specialty of this type of support because of this type of support there will be two reactions one vertical as well as one horizontal reaction so let's call the vertical reaction as r -a -y plus the horizontal reaction let's call the horizontal one, the horizontal reaction as r -a -x.

01:42 Now for the trans -b in point o, point o, there is a recent support, that is a pin support.

02:01 We know the specialty of pin support because this type of support, there will be two reactions, one vertical as well as one so the let's call the vertical reaction as r -o -y and the horizontal reaction.

02:24 Let's call it as r -o -x.

02:28 And in point a also, in point a also there is a pin support.

02:38 So because the type of support is pinned one, there is two type of two reactions.

02:47 This causes two reactions.

02:52 One vertical, let's call it as r -a -y, plus one horizontal.

03:02 Let's call this one the horizontal one as r -a -x.

03:16 Now let's denote the forces here in the diagram itself.

03:26 This is r -r -y...