All questions of Plane Trusses for Mechanical Engineering Exam

Explanation:
The statement in question states that there are no rules for designing a truss, but there are rules for designing bridges. The correct answer is option B, which means that the first part of the statement is false and the second part is also false.

Designing a truss:
A truss is a structural framework that consists of straight members connected at joints. Trusses are commonly used in engineering and construction to support loads such as the weight of a roof or a bridge. While there may not be specific rules for designing a truss, there are certainly principles and guidelines that need to be followed to ensure the structural integrity and stability of the truss. These principles include:

1. Analysis of loads: The first step in designing a truss is to analyze the loads that the truss will be subjected to. This includes considering the weight of the structure, any live loads such as people or vehicles, wind loads, and seismic loads. The truss must be designed to safely support these loads without excessive deflection or failure.

2. Material selection: The choice of materials for the truss is important to ensure its strength and durability. Common materials used for truss construction include steel, timber, and aluminum. The material must be able to withstand the loads and environmental conditions that the truss will be exposed to.

3. Truss configuration: The configuration of the truss, including the arrangement and size of the members and the connections between them, is crucial for its stability and load-bearing capacity. Various truss configurations, such as the Pratt truss, Warren truss, and Howe truss, have different advantages and limitations, and the appropriate configuration should be chosen based on the specific requirements of the project.

4. Structural analysis: Once the truss configuration is determined, it is important to perform structural analysis to ensure that the truss can safely carry the imposed loads. This analysis involves calculations to determine the internal forces and stresses in the truss members, as well as deflections and deformations. Finite element analysis (FEA) software is commonly used for this purpose.

Designing a bridge:
The second part of the statement is also false. There are indeed rules and guidelines for designing bridges. Bridges are complex structures that must safely support the weight of vehicles, pedestrians, and other loads while spanning across rivers, valleys, or other obstacles. The design of a bridge involves several considerations, including:

1. Structural analysis: Similar to truss design, a bridge must undergo structural analysis to ensure its stability and load-bearing capacity. This analysis considers the forces and stresses that the bridge will experience, including dead loads, live loads, wind loads, and seismic loads.

2. Material selection: The choice of materials for the bridge depends on factors such as span length, anticipated loads, and environmental conditions. Common bridge materials include steel, concrete, and composite materials. The material must have sufficient strength, durability, and resistance to corrosion.

3. Bridge type and configuration: Different types of bridges, such as beam bridges, arch bridges, and suspension bridges, have different structural characteristics and requirements. The selection of the appropriate bridge type and configuration depends on factors such as span length, terrain, and budget.

4. Geotechnical considerations: Bridges often require foundations to support their weight. Geotechnical investigations are conducted to assess the soil and rock conditions at the bridge site, which helps determine the appropriate foundation design, such as

False

Explanation:

Free Body Diagrams:
Free body diagrams are used to represent the external forces acting on a body or a system. These diagrams are used to analyze the equilibrium of the body or system by considering the forces and their directions. In a free body diagram, all forces acting on the body are represented by vectors. These forces can include both translational forces (such as applied loads, reactions, etc.) and rotational moments (such as torques).

Internal Forces:
Internal forces are forces that exist within a body or a system. These forces are not visible from the outside and are responsible for maintaining the equilibrium of the body. When analyzing internal forces using the method of sections, a section is cut through the body or system to isolate a portion of it. The internal forces at the cut section are then evaluated to determine their magnitude, direction, and type (such as tension, compression, shear, etc.).

Rotational Moments:
Rotational moments, also known as torques, are forces that cause an object to rotate about an axis. These moments are typically caused by external forces acting at a distance from the axis of rotation. Rotational moments are important in analyzing the equilibrium of a body or system, especially when considering the rotational motion.

Importance of Rotational Moments:
Rotational moments are essential in analyzing the equilibrium of a body or system. They play a crucial role in determining the stability, balance, and motion of the body. Ignoring rotational moments in free body diagrams or the evaluation of internal forces by the method of sections can lead to incorrect results and an incomplete understanding of the system's behavior.

Conclusion:
In conclusion, rotational moments are indeed counted in free body diagrams and the evaluation of internal forces by the method of sections. These moments are essential in analyzing the equilibrium and motion of a body or system. Therefore, the statement "Rotational moments are not counted in the free body diagrams and the evaluation of the internal forces by the method of sections" is false.

Internal Forces in the Method of Sections

In the method of sections, which is commonly used for analyzing complex truss structures, the internal forces within the members of the structure are determined by applying the principle of equilibrium to a section of the truss. This allows us to calculate the internal forces such as axial forces, shear forces, and bending moments in the members.

External Forces
The external forces are the forces acting on the truss that are not located within the section under consideration. These forces include applied loads, reactions at supports, and any external moments. The external forces are applied to the truss as a whole and are not specifically related to the section being analyzed.

Method of Sections
The method of sections involves cutting the truss into two sections by passing an imaginary line through the desired section. This imaginary line is called the section line. By isolating one of the sections and considering the equilibrium of forces acting on that section, we can determine the internal forces within the members of the truss.

Calculation of Internal Forces
To calculate the internal forces in the method of sections, we consider the equilibrium of forces acting on the isolated section. This includes both external forces and internal forces within the members. By applying the equations of equilibrium, such as the sum of forces in the x-direction and sum of forces in the y-direction, we can solve for the unknown internal forces.

Choice of External Forces
In the method of sections, we only consider the external forces acting on the truss as a whole. This is because the internal forces within the members are a result of the equilibrium of these external forces. By neglecting the internal rotational forces and considering only the external forces, we can simplify the analysis and focus on determining the internal forces within the members.

Therefore, the correct answer is option 'D' - External forces.

Bridge structures are designed to transmit loads from stringers to floor beams and then to joints.

There is normal component of force acting o the body. though there is bending moment by external force, which is resisted by the normal stress generated by itself. so the answer is 0

Stability Improvement with Zero Forces
Improving the stability of a structure is crucial to ensure its safety and longevity. Zero forces are utilized in structural design to enhance stability by minimizing or eliminating the effects of external forces acting on the structure.

Role of Zero Forces in Stability:
- Zero forces are strategically introduced into the structure to counteract external forces such as wind loads, seismic forces, or live loads.
- By distributing these zero forces effectively throughout the structure, the overall stability is enhanced, reducing the likelihood of structural failure or collapse.

Benefits of Stability Enhancement:
- Increased resistance to lateral forces: Structures with improved stability can better withstand lateral forces, such as wind or seismic loads, without experiencing excessive deformation or damage.
- Enhanced load-carrying capacity: A stable structure can efficiently distribute loads, preventing localized stress concentrations and ensuring uniform load transfer throughout the system.
- Improved overall performance: Stability improvements contribute to the overall performance of the structure, increasing its reliability and safety under various loading conditions.
In conclusion, the utilization of zero forces plays a significant role in enhancing the stability of a structure, ultimately ensuring its structural integrity and longevity. By effectively managing external forces through the incorporation of zero forces, engineers can optimize the performance and safety of the structure.

Shear force
The force acting parallel/tangential to the beam is called shear force. Let's break down the concept in detail:

Definition
Shear force is the force that acts parallel to the surface of a material, such as a beam. It creates a sliding or tearing effect on the material, causing it to deform.

Causes
Shear force is typically caused by external loads applied to a structure, such as bending moments or direct forces. These forces can result in shear stress within the material.

Effects
Shear force can lead to deformation or failure of a material if it exceeds the material's shear strength. It is crucial to consider shear force in the design and analysis of structures to ensure their stability and safety.

Calculation
Shear force can be calculated at any point along a beam using equilibrium equations. It is represented by the symbol V and is measured in units of force (e.g., Newtons or pounds).

Application
Understanding shear force is essential in civil and mechanical engineering, as it influences the design, analysis, and performance of structures like bridges, buildings, and machinery.
In summary, shear force plays a significant role in the behavior of materials and structures. By considering shear force in design and analysis processes, engineers can ensure the safety and reliability of their creations.

The truss is a structure made of slender members which are joined together at their end points. They can be of wooden or steel. But most probably they are made from stainless steel. As they need to support the loadings in various climates.

Explanation:

First Step:
- The determination of the truss's support reaction is done first.
- This step involves analyzing the external forces acting on the truss structure and calculating the support reactions at the points where the truss is connected to the external supports.
- These support reactions help in determining the stability and equilibrium of the truss structure.

Second Step:
- Then the section is isolated for the method of the section.
- Once the support reactions are determined, the truss structure can be analyzed further by isolating a specific section of the truss.
- The method of sections is used to analyze the internal forces (such as member forces) within the isolated section of the truss.
- This step helps in determining the forces acting on individual members of the truss structure.
Therefore, the correct approach is to first determine the support reactions of the truss and then isolate a section for further analysis using the method of sections. This sequential process ensures a systematic and accurate analysis of the truss structure.

Support loads refer to the forces or loads that are applied to a structure to ensure its stability and resistance to external forces. These loads are crucial in preventing the structure from collapsing or deforming under the applied loads. In engineering, various structural elements are used to provide support and distribute these loads effectively. Some of the commonly used structural elements for support loads are frames, machines, trusses, and beams.

Frames:
- Frames are structural elements that consist of interconnected bars or beams arranged in a rigid framework. They are used to support loads by transferring the applied forces to the foundations or other supporting structures.
- Frames can be made of various materials such as steel, concrete, or timber, depending on the application and the required strength.
- Frames are commonly used in buildings, bridges, and other structures where the loads need to be distributed and transferred efficiently.

Machines:
- Machines, such as cranes, hoists, and lifts, are often used to support heavy loads and move them from one place to another.
- These machines are designed with strong structural components, such as beams and frames, to provide the necessary support and stability.
- The structural elements in machines are specifically designed to withstand the dynamic forces and vibrations generated during the operation.

Trusses:
- Trusses are structural elements composed of interconnected triangular units. They are commonly used to support loads in roofs, bridges, and other structures.
- The triangular units in trusses distribute the applied loads evenly along the members, making them highly efficient in supporting large loads.
- Trusses are lightweight and can span long distances, making them an ideal choice for structures where weight and span are critical factors.

Beams:
- Beams are horizontal or vertical structural elements that are used to support loads by transferring them to the supports or foundations.
- Beams are often made of materials such as steel, concrete, or timber, depending on the required strength and the specific application.
- Beams can be simple or composite, depending on the complexity of the load distribution and the structural requirements.

In conclusion, frames, machines, trusses, and beams are all used as support loads in various engineering applications. Each of these structural elements serves a specific purpose in providing stability, distributing loads, and ensuring the overall structural integrity of the system.

C) The direction of the unknown force cannot be determined

The correct answer is option 'C': The first part of the statement is true and the other part is false.

Explanation:

Method of Joints:
The method of joints is a technique used to analyze trusses by considering the equilibrium of each joint. It allows us to determine the unknown forces acting on the joints of the truss. By applying the principles of statics, we can solve for these unknown forces by considering the forces in equilibrium at each joint.

Method of Sections:
The method of sections is another technique used to analyze trusses. It involves cutting the truss into two sections and analyzing the equilibrium of one of the sections to determine the unknown forces. This method allows us to calculate the forces in members that are not directly connected to the joints.

Correcting the statement:
The first part of the statement is true because the method of joints does help us find out the unknown forces in the truss joints. However, the second part of the statement is false. The method of sections is not used to calculate the direction of the zero members. Instead, it is used to determine the forces in members that are not directly connected to the joints.

The correct statement should be:
"The method of joints helps us to find out the unknown forces in the truss joints. However, the method of sections is used to calculate the forces in members that are not directly connected to the joints, not the direction of the zero members."

In conclusion, while the first part of the statement is true, the second part is false. The method of sections is not used to calculate the direction of the zero members in trusses.

Explanation:

When bridges are extended over long routes or distances, it is important to consider the effects of temperature changes on the structure. The expansion and contraction of the bridge due to temperature changes can cause stress and potential damage to the joints. To mitigate these effects, engineers often incorporate rockers or rollers at the joints.

Rockers and Rollers:

Rockers and rollers are types of bearings that allow for movement and rotation at the joints of a bridge. A rocker bearing is designed to allow rocking motion, while a roller bearing allows for rolling motion. Both types of bearings provide flexibility and accommodate the thermal expansion and contraction of the bridge.

Effects of Temperature:

When the temperature of the bridge increases, the materials expand. Conversely, when the temperature decreases, the materials contract. These thermal movements can lead to significant displacements and stresses at the joints of the bridge.

Benefits of Rockers and Rollers:

By incorporating rockers or rollers at the joints, the elongations and contractions of the joint parts are not significantly affected by temperature changes. This is because the rockers and rollers allow the bridge to move and adjust freely in response to temperature variations. The bearings effectively absorb the thermal movements, reducing the stress on the joints and preventing potential damage.

Flexibility and Safety:

Using rockers or rollers at the joints provides the bridge with the necessary flexibility to accommodate thermal expansion and contraction. This flexibility ensures the safety and integrity of the structure, as it minimizes the risk of excessive stress concentrations and potential failure.

Conclusion:

Therefore, the statement "When the bridges are extended over long routes or distance, a rocker or a roller is used at the joints. As when the temperature is raised, the elongations and the contractions of the joints part are not much affected if the rollers and rockers are used" is true. Rockers and rollers provide the necessary flexibility and allow for the smooth movement of the bridge, minimizing the impact of temperature changes on the joints.

Explanation:

The correct answer is option 'C', which states that the first part of the statement is true and the other part is false. Let's break down the explanation:

- Method of section:
- The method of section is a technique used in structural analysis to determine the internal forces within a truss by cutting the structure into sections and analyzing the equilibrium of the section.

- False Statement:
- The first part of the statement, which says that the whole structure of trusses is cut into a section, is false. In reality, the method of section involves cutting a specific section of the truss where the unknown forces need to be calculated.

- True Statement:
- The second part of the statement, which mentions that at most two forces must be collinear, is true. When applying the method of section, the equilibrium of the section is analyzed by considering at most two unknown forces that are collinear. This simplifies the calculations and makes it easier to solve for the unknown forces.

In conclusion, the method of section is a powerful tool in analyzing truss structures, but it involves cutting a specific section of the truss rather than the entire structure. Additionally, the method requires at most two forces to be collinear for accurate calculations.