SOLID STRUCTURES 1PIN-JOINTED FRAMES, Exams of Engineering Physics

Download SOLID STRUCTURES 1PIN-JOINTED FRAMES and more Exams Engineering Physics in PDF only on Docsity!

SIMPLE TRUSSES, THE

METHOD OF JOINTS,

& ZERO-FORCE MEMBERS

Objectives:

Students will be able to: a) Define a simple truss. b) Determine the forces in members of a simple truss. c) Identify zero-force members.

APPLICATIONS (continued)

Trusses are also used in a variety of structures like cranes and the frames of aircraft or the space station. How can you design a light weight structure satisfying load, safety, cost specifications, is simple to manufacture, and allows easy inspection over its lifetime?

SIMPLE TRUSSES

If a truss, along with the imposed load, lies in a single plane (as shown at the top right), then it is called a planar truss. A truss is a structure composed of slender members joined together at their end points. A simple truss is a planar truss which begins with a triangular element and can be expanded by adding two members and a joint. For these trusses, the number of members (M) and the number of joints (J) are related by the equation M = 2 J – 3.

Introduction

6 - 8

• For the equilibrium of structures made of several connected parts, the internal forces as well the external forces are considered.
• In the interaction between connected parts, Newton’s 3 rd Law states that the forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense.
• Three categories of engineering structures are considered: a) Frames : contain at least one multi-force member, i.e., member acted upon by 3 or more forces. b) Trusses : formed from two-force members , i.e., straight members with end point connections c) Machines : structures containing moving parts designed to transmit and modify forces.

2 - 10 Consider parts of the column External Forces Internal Forces (to the column AB) From 2 to 1 From 1 to 2 Load reaction Ay= 100N Ay= 100N 100N 100N 100N A B FBD

6 - 11

• Dismember the truss and create a freebody diagram for each member and pin.
• The two forces exerted on each member are equal, have the same line of action, and opposite sense.
• Forces exerted by a member on the pins or joints at its ends are directed along the member and equal and opposite.
• Conditions of equilibrium on the pins provide 2 n equations for 2 n unknowns. For a simple truss, 2 n = m + 3. May solve for m member forces and 3 reaction forces at the supports.
• Conditions for equilibrium for the entire truss provide 3 additional equations which are not independent of the pin equations.

THE METHOD OF JOINTS

When using the method of joints to solve for the forces in truss

members, the equilibrium of a joint (pin) is considered. All

forces acting at the joint are shown in a FBD. This includes all

external forces (including support reactions) as well as the forces

acting in the members. Equations of equilibrium (å F

X

= 0 and

å F

Y

= 0) are used to solve for the unknown forces acting at the

joints.

A free-body diagram of Joint B

STEPS FOR ANALYSIS

1. If the truss’s support reactions are not given, draw a FBD of

the entire truss and determine the support reactions (typically

using scalar equations of equilibrium).

2. Draw the free-body diagram of a joint with one or two

unknowns. Assume that all unknown member forces act in

tension (pulling on the pin) unless you can determine by

inspection that the forces are compression loads.

3. Apply the scalar equations of equilibrium, å F

X

= 0 and

å FY = 0, to determine the unknown(s). If the answer is

positive, then the assumed direction (tension) is correct,

otherwise it is in the opposite direction (compression).

4. Repeat steps 2 and 3 at each joint in succession until all the

required forces are determined.

ZERO – FORCE MEMBERS (continued)

Again, this can easily be proven. One can

also remove the zero-force member, as

shown, on the left, for analyzing the truss

further.

Please note that zero-force members

are used to increase stability and

rigidity of the truss, and to provide

support for various different loading

conditions.

If three members form a truss joint for

which two of the members are collinear

and there is no external load or reaction at

that joint, then the third non-collinear

member is a zero force member, e.g., DA.

EXAMPLE

1. Check if there are any zero-force members.
2. First analyze pin D and then pin A
3. Note that member BD is zero-force member. FBD = 0
4. Why, for this problem, you do not have to find the external reactions before solving the problem? Given : Loads as shown on the truss Find: The forces in each member of the truss. Plan:

EXAMPLE (continued)

• ® å FX = FAB + (– 318) cos 45° = 0; FAB = 225 lb (T) Could you have analyzed Joint C instead of A? 45 º FAB A FBD of pin A

FAD

AY

Analyzing pin A:

Using the method of joints, determine the force in

each member of the truss.