Truss MCQ Quiz in मराठी - Objective Question with Answer for Truss - मोफत PDF डाउनलोड करा

Concept:

Perfect truss:

A truss which has enough members to resist the load without deformation in its shape is called a perfect truss. A triangular truss is the simplest perfect truss and has three joints and three members.

Condition for perfect truss

\(M=2j-3\)

Where M = Number of members

j = Number of joints

Important points:

• \(M>2j-3\,\, Redundent\)
• \(M<2j-3\,\,Deficient\)

Explanation:

Given

Number of member in given figure (M) = 9

Number of joint in given figure (j) = 6

2j - 3 = 2 × 6 - 3 = 9

\(2j-3=9\)

M = 2j - 3

Hence the given figure of truss in the question is a perfect truss.

Explanation:

In general, let a frame have j joints and m members.

If m + r = 2j , then the frame is perfect frame.

If m + r < 2j , then the frame is deficient frame.

If m + r > 2j , then the frame is redundant frame.

A perfect frame can always be analyzed by the condition of equilibrium. While a redundant frame cannot be fully analyzed by the condition of equilibrium.

Hence, If in a pin-jointed plane frame (m + r) > 2 j, then the frame is stable and statically indeterminate.

Additional InformationThe static indeterminacy for frames under different conditions are:

1. Pin Jointed space Frame (3D)

Ds = m + r - 3j

2. Pin Jointed Plane Frame (2D)

Ds = m + r - 2j

 3. Rigid Jointed Plane Frame (2D):

DS = 3m + r - 3j - R;

4. Rigid Jointed Space Frame (3D):

DS = 6m + r - 6j - 3R;

Where,

m is the no of members

r is no. of support reactions

R is total no. of releases

J is the nos. of joints

Calculation:

Given structure in below figure:

Now draw the free body diagram of point B

Hence, apply the equilibrium for forces in the vertical direction 

\(\sum F_y =0\)

F_CB Sin30 = 2t

F_CB \(\times \ {1 \over 2}\) = 2t

F_CB = 4t

Concept-

Conditions for zero force members-

• At a two member joint, if the members are not parallel and there are no other external loads (or reactions) at the joint then both of those members are zero force members.
• 

• In a three member joint, if two of those members are parallel and there are no other external loads (or reactions) at the joint then the member that is not parallel is a zero force member.

• 

Given data and Analysis-

As per condition 2, the zero force members are -

DE = EF = FG =GH = LM = LK = KJ = 0

Truss: It is defined as a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.

Truss can be classified as follows:

a) Simple Truss: It consists of a series of triangles so that the weight being supported is distributed evenly to the supports.

b) Complex Truss: It is not necessarily a set of the triangle as the members may overlap each other.

Given above is an example of a complex truss.

Concept:

If two non-collinear members meet at a joint, and there is no force at that joint then the forces on two members will be zero.

Truss Member Carrying Zero forces

i) M1, M2, M3 meet at a joint M1 & M2 are collinear.

⇒ M3 carries zero force.

Where M1, M2, M3 represents member.

ii) M1 & M2 are non collinear and Fext = 0

⇒ M1 & M2 carries zero force.

For the given truss, these members are zero:

∴ No. of members having zero forces = 15

A truss is defined as a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.

The most simple type of truss is a triangle truss.

Simple trusses consist of a series of triangles so that the weight being supported is distributed evenly to the supports.

Some of the different types of simple trusses are as follows:

​

∴ The simple truss may consist of any other shaped intermediate parts, as long as it is stable.

∴ Both statements A and B are correct.

Explanation

The objective of truss analysis is to determine the reactions and member forces. The methods used for carrying out the analysis with the equations of equilibrium and by considering only parts of the structure through analyzing its free body diagram to solve the unknowns.

The assumptions made in the analysis of truss -

• Truss members are connected together at their ends only.
• Truss are connected together by frictionless pins.
• The truss structure is loaded only at the joints.
• The weights of the members may be neglected.
• The bending resistance of all the members is small in comparison with their axial force resistance.
• At any joint, the axes of all members meeting pass through a single point

There are various methods to analyze a truss considering the above mentioned assumptions. They are:

• Method of joints,
• Method of sections.

Explanation:

A truss is a network of longitudinal members joined at ends.

Applications: Roofs, bridges, and towers.

Types of truss:

Perfect truss:

It is rigid and statically determinate.

For a truss to be perfect, the condition is:

m + 3 = 2J.

Imperfect truss

• Redundant truss: A truss that is imperfect due to the presence of more members than required is known as a redundant truss.
• Condition for redundant truss is

m + 3 > 2j,

where m and j are members and joints respectively

• Deficient truss: A truss that is imperfect due to the presence of fewer members than required is known as a Deficient truss.
• Condition for deficient truss is

m + 3 < 2j

members (m) = 14

joints (j) = 9

14 + 3 < 2 × 9

17 < 18 (deficient truss)

Concepts:

A truss that has a sufficient number of members to maintain its stability and satisfies equilibrium conditions is called a statically determinate and stable truss, otherwise, it is statically indeterminate.

Let m = total no of members, r = no of reactions = 3 in 2D truss, J = no of joints

If m + 3 < 2j then the truss is unstable.

If m+ 3 = 2j then truss is statically determinate and stability is checked by visual inspection.

If m + 3  > 2j then the truss is statically indeterminate and stability is checked by visual inspection.

It is given in the question that the truss is pin jointed plane frame i.e. it lies in 2D, so generally, no of reactions involved are 3 ( two at pin support and 1 at roller support). Therefore, m > 2j-3 implies that the truss is statically indeterminate.