Elements Of Mechanical Engineering Quiz

The statement is true. A roller is indeed provided at the end of a bridge truss to allow for thermal expansion. Bridges are subject to temperature changes, which can cause the bridge to expand or contract. By providing a roller at the end of the truss, it allows the bridge to move freely and accommodate these changes without causing any structural issues or damage.

The degree of kinematic indeterminacy of a pin-jointed plane frame is given by 2j-r. This formula represents the number of unknown displacements (2j) minus the number of reactive forces (r). In a pin-jointed plane frame, there are 2j unknown displacements because each joint has two degrees of freedom (horizontal and vertical displacements). The reactive forces (r) are the external forces applied to the frame. Therefore, the correct answer is 2j-r.

When a member of a truss is in compression, it means that it is being pushed together, causing the member to shorten. In this case, the force that the member applies to the joints will be directed outward. This is because the member is pushing against the joints, exerting a force away from the center of the truss.

In order for both members to be zero force members, they must be in a state of equilibrium. This means that the forces acting on each member must be balanced and cancel each other out. In a system where both members are zero force members, the angle between them would be 90 degrees. At this angle, the forces acting on each member would be perpendicular to each other, resulting in a balanced system.

The degree of static indeterminacy of a pin-jointed plane frame is given by the formula m+r-2j. This formula takes into account the number of unknown member forces (m), the number of unknown reaction components (r), and the number of joints (j) in the frame. By subtracting twice the number of joints from the sum of the unknown member forces and unknown reaction components, we can determine the degree of static indeterminacy.

Trusses and frames are different in terms of their ability to bend. Trusses cannot bend, while frames have the capability to bend. This means that trusses are rigid structures that do not experience any deformation under load, whereas frames have some flexibility and can undergo bending when subjected to external forces.

In a truss, it is assumed that the members are joined by smooth pins. Smooth pins allow for rotational motion at the joints, which helps distribute forces evenly throughout the truss structure. This assumption simplifies the analysis of the truss, as it eliminates the need to consider friction or resistance to rotation at the joints. Additionally, smooth pins allow for easier assembly and disassembly of the truss, making it a practical choice for construction purposes.

Concrete is not used in making trusses because trusses are typically made using lightweight materials such as wood or metal bars. Concrete is a heavy and rigid material that is more commonly used in construction for its strength and durability in supporting structures, such as foundations or columns. Trusses, on the other hand, are designed to distribute loads and provide stability, and materials like wood or metal bars are better suited for this purpose due to their lighter weight and flexibility.

In order for a structure to be stable, the equilibrium equations should be concurrently satisfied in all the joints. Since there are a total of 10 joints in the structure, the minimum number of joints in which the equilibrium equations should be satisfied for stability is 10. This means that all 10 joints need to be in equilibrium for the structure to be stable.

If the sum of the number of members (m) and the number of reactions (r) in a pin-jointed plane frame is less than twice the number of joints (2j), then the frame is considered unstable.

The given question does not provide enough information to determine the stability or determinacy of the system. The number of reactions alone is not sufficient to make a conclusion about the stability or determinacy of the beam. Additional information about the supports, loads, and geometry of the beam would be needed to determine the system's stability and determinacy. Therefore, it is not possible to say whether the system is stable or determinate based on the given information.

The force in member BC of the truss is 707.1 N. This is because the truss is in equilibrium, meaning that the sum of forces acting on it is zero. Member BC is the only member that is not vertical or horizontal, so it carries both vertical and horizontal forces. By analyzing the forces acting on the truss, it can be determined that the vertical component of the force in member BC is equal to the vertical force acting at joint B, which is 707.1 N.

The vertical reaction force at Point A of the truss is 600 N because it is the only force that can counterbalance the vertical forces acting on the truss. The truss is in equilibrium, meaning that the sum of the vertical forces must be zero. Since there is a downward force of 200 N acting at Point A and an upward force of 400 N acting at Point A, the vertical reaction force at Point A must be 600 N to balance out these forces.

In the given system, a zero force member is a member that does not carry any force and is in equilibrium. In this case, we can observe that the members AC, AD, AE, AF, AG, AH, AI, AJ, and AK are all zero force members because they are not connected to any external force and do not carry any load. Therefore, the total number of zero force members in the system is 9.

In the given figure, the support reaction at point B is determined by the principle of equilibrium. The sum of all the vertical forces acting on the beam must be equal to zero. Since there is a 900 N force acting downwards at point B, the support reaction at B must be equal in magnitude but in the opposite direction, i.e., 900 N upwards. This ensures that the beam remains in equilibrium and does not rotate.

The force in member AC of the truss is 500 N.

In trusses, a member in the state of tension can be subjected to either pull or push forces. This means that the member can experience forces that tend to elongate or compress it. The specific type of force (pull or push) will depend on the specific configuration and loading conditions of the truss. Therefore, the member can be subjected to either a pulling force or a pushing force, depending on the circumstances.

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If a structure has 2j - r number of members, then it will be stable. The stability of a structure is determined by the balance of forces acting on it. In this case, the number of members is greater than the number of external forces, which suggests that there are enough supports and connections to distribute the forces evenly and maintain the stability of the structure.

In a space structure, static equilibrium requires that the sum of all forces and moments acting on the structure be equal to zero. This can be achieved by satisfying the equations of equilibrium, which include three force equations and three moment equations. Therefore, a total of six independent equations need to be satisfied for static equilibrium in a space structure.