Civil Engineering Questions On Theory Of Structure

Gradually applied static loads do not change with time in terms of their magnitude, direction, or point of application. This means that these loads remain constant throughout the duration of their application, without any variation in their strength, orientation, or location. Therefore, the correct answer is "all the above" as all the mentioned aspects (magnitude, direction, and point of application) remain unchanged for gradually applied static loads.

A body is said to be in equilibrium when the net force acting on it is zero. This means that the body is not moving horizontally or vertically, and it is also not rotating about its center of gravity. In other words, the body is in a state of balance where all the forces acting on it cancel each other out, resulting in no net force or movement. Therefore, the correct answer is "none of these" as none of the given options accurately describe the condition of equilibrium.

The principle of virtual work can be applied to an elastic system by considering the virtual work of both internal and external forces. This principle states that the work done by all forces acting on a system, including both internal and external forces, is equal to zero for a system in equilibrium. By considering both internal and external forces, the principle of virtual work allows for a comprehensive analysis of the elastic system, taking into account all the forces that contribute to its equilibrium.

Both a and b are correct statements. A flexibility matrix is a square symmetrical matrix, meaning that it is a matrix with equal number of rows and columns, and its elements are symmetric with respect to the main diagonal. Similarly, a stiffness matrix is also a square symmetrical matrix.

When a force is applied on an inclined plane, it can be resolved into two components: normal and tangential. The normal component acts perpendicular to the plane, while the tangential component acts parallel to the plane. In order for the normal and tangential components of stress to be equal, the inclined plane must be at an angle of 45° to the direction of the force. At this angle, the force is evenly distributed between the two components, resulting in equal stress.

In a rigid jointed plane frame, the number of unknown internal forces in each member can be determined using the equation 2j - 3, where j is the number of joints. Since a rigid jointed plane frame typically has 3 joints, plugging this value into the equation gives us 2(3) - 3 = 6 - 3 = 3. Therefore, the correct answer is 3.

For a plane structure to be in static equilibrium, the sum of forces in both the horizontal and vertical directions must be zero, and the sum of moments about any point must also be zero. These conditions give rise to three independent equations that need to be satisfied for static equilibrium. Therefore, the correct answer is 3.

The statement "All the above" is the correct answer because it includes all the given statements. The moment of inertia is indeed calculated about the axis about which bending takes place. If the tensile stress is less than the axial stress, it means that the section is experiencing compressive stress. Similarly, if the tensile stress is equal to the axial stress, the section also experiences compressive stress. Lastly, if the tensile stress is more than the axial stress, it implies that some portion of the section experiences tensile stress. Therefore, all the statements are true.

The section modulus of a beam is a measure of its resistance to bending. It is calculated by dividing the moment of inertia of the section by the distance from the neutral axis to the outermost point of the section. The neutral axis is the line within the section where the stress and strain are zero, and it is the axis about which the beam tends to rotate when subjected to bending. Therefore, the correct answer is the depth of the neutral axis, as it is directly related to the section modulus calculation.

In a rigid jointed space frame, if the sum of the number of members (m) and the number of reactions (r) is less than the number of joints (j), then the frame is stable but statically indeterminate. This means that the frame is able to support external loads and maintain its equilibrium, but the internal forces in the members cannot be determined solely from the equilibrium equations. This is because there are more unknowns (internal forces) than the number of equations available.

In the moment distribution method, the sum of the distribution factors of all the members meeting at any joint is always one. This means that the total moment applied at a joint is distributed among the members in such a way that the sum of the moments in each member equals the applied moment at that joint. This ensures equilibrium and allows for the calculation of member end moments in a structural analysis.

The displacement method is a structural analysis technique used to determine the displacements and forces in a structure. It involves calculating the displacements of each member of the structure and then using these displacements to determine the forces in each member. The equilibrium method, moment distribution method, and Kani's method are all displacement methods commonly used in structural analysis. However, the column analogy method is not a displacement method. Instead, it is a simplified method used to analyze and design columns in a structure. It involves comparing the behavior of a column to that of a simple beam or column, making it a different approach than the displacement methods.

When a beam is subjected to a concentrated load at its center, the deflection is directly proportional to the load applied. In this case, the original beam deflects by 5mm when a load of 10KN is applied. Since the model beam is a 1/10 scale of the original beam, the load applied to the model beam is 1KN. As the load is reduced by a factor of 10, the deflection will also be reduced by the same factor. Therefore, the deflection in the model beam will be 5mm, which is the same as the deflection in the original beam.

The product of moment of inertia is zero because the principal axes of a section are the axes along which the moment of inertia is maximum or minimum. Since the product of moment of inertia is defined as the sum of the products of the mass of each particle in the body and the square of its distance from the axis of rotation, if the product of moment of inertia is zero, it means that the mass particles are either located on the axis of rotation or their distances from the axis are zero.

The correct answer is 4 because when both ends of a column are fixed, it is more rigid and can withstand higher loads compared to when both ends are hinged. The ratio of the crippling loads of the fixed column to the hinged column is 4, indicating that the fixed column can bear four times more load than the hinged column before it fails.