Truss MCQ Quiz in తెలుగు - Objective Question with Answer for Truss - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

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:

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)

Concept:

Planar Truss: When all the members and nodes of a truss lie within a 2-dimensional plane it is called a planar truss.

Members of a truss carry only axial force. If the member of a truss does not carry any force under some specific load conditions, those members are called zero-force members.

Identification of zero-force members:

1) If at any joint two members are non-collinear and no load is acting at the joint, then both the members will be zero-force members.

e.g.

In the truss shown above, there are two non-collinear members at joint D and there is no load acting at this joint, hence both the members BD and CD are zero force members.

2) If at a truss joint, 3 members are meeting and two of them are collinear and no load is acting at the joint, then the non-collinear member will be a zero-force member.

e.g.

Explanation:

From the figure, as we can see that there is no any load external member AD and AB.

If only two non-collinear members exist at a truss joint and no external force or support reaction is applied to the joint, the member must be zero force members.

Hence the force in the member AB = Zero

Concept:

• The analysis of trusses is usually based on the following simplifying assumptions.

1. The centroidal axis of each member coincides with the line connecting the centers of the adjacent members and the members only carry axial force.
2. All members are connected only at their ends by frictionless hinges in plane trusses.
3. All loads and support reactions are applied only at the joints.

• The reason for making these assumptions is to obtain an ideal truss, i.e., a truss whose members are subjected only to axial forces
• Types of forces in a truss are as follows

1. Primary Forces =member axial forces determined from the analysis of an ideal truss.
2. Secondary Forces = deviations from the idealized forces, i.e., shear and bending forces in a truss member.

         Our focus will be on primary forces. If large secondary forces are anticipated, the truss should be analyzed as a frame.

Calculation:

Given 

Load, P = 10 kN acts on joint B, AB = 1 m, AC = 0.5 m,

Let reactions at A in a vertical and horizontal direction as v_A and H_A  respectively

NOTE: Forces in truss as generally assumed as tensile. So, in truss analysis, positive member force means tensile force in that member and negative member force means compressive force in that member.

 ∑ M_C = 0, Taking moment about point C

= H_A×0.5 + 10×1 = 0 ( Moment of V_A  about C  will be 0 )

= H_A = -10/0.5 = -20 kN

∑ H_A = 0, Take sum of Horizontal forces as zero at joint A

= H_A + F_AB = 0

= - 20 + F_AB = 0

= F_AB = 20 kN and the nature of force is tensile as force comes out positive.

Important Points

• Method to identify zero force members in a given truss

1. If only two noncollinear members are connected to a joint that has no external loads or reactions applied to it, then the force in both members is zero.
2. If three members, two of which are collinear, are connected to a joint that has no external loads or reactions applied to it, then the force in the member that is not collinear is zero.