Title Mechanical Important Questions.pdf ✅

IMPORTANT QUESTIONS & ANSWERS_BME-101 Q.1 State principle of transmissibility. Answer: Principle of transmissibility of forces Principle of transmissibility states that the state of rest or of motion of a rigid body will be unaltered if a force acting on the body will be replaced by another force of the same magnitude and direction but acting anywhere on the body along the same line of action of the applied forces. For example the force F acting on a rigid body at point A. According to the principle of transmissibility of forces, this force has the same effect on the body as a force F applied at point B. The principle of transmissibility of forces will be only applicable for rigid bodies. It will not be applicable for deformable bodies. Q.2 State and proof Varignon’s theorem. A. Principle of moment/ Varignon’s theorem Varignon’s Theorem states that the moment of a force about any point is equal to the algebraic sum of the moments of its components about that point. Principal of moments states that the moment of the resultant of a number of forces about any point is equal to the algebraic sum of the moments of all the forces of the system about the same point. Mathematically R x AD = P x AB + Q x AC Taking components of forces R sin θ = P sin θ1 + Q sin θ2 ............ (i) Multiplying both side by OA
R (OA sin θ) = P (OA sin θ1) + Q (OA sin θ2)............ (ii) R x AD = P x AB + Q x AC ............ (iii) Q.3 Define free body diagram. A. A diagram or sketch of the body in which the body under consideration is freed from the contact surface (surrounding) and all the forces acting on it (including reactions at contact surface) are drawn is called free body diagram. Free body diagram for few cases are shown in below Q.4 Define Equilibrium of bodies. What are the conditions of equilibrium? A. Equilibrium of coplanar force system If the force system acting on a body produces no external effect, the forces are said to be in balance and the body experience no change in motion is said to be in equilibrium. Conditions of Static Equilibrium of Concurrent Forces The algebraic sum of all forces in the x-direction or horizontal is zero. The algebraic sum of all forces in the y-direction or vertical is zero. Important Points for Equilibrium Forces Two forces are in equilibrium if they are equal and oppositely directed. Three coplanar forces in equilibrium are concurrent. Three or more concurrent forces in equilibrium form a close polygon when connected in head-to-tail manner. Conditions of Static Equilibrium of Non-Concurrent Force System There are three equilibrium conditions that can be used for non-concurrent, non-parallel force system. The algebraic sum of all forces in the x-direction or horizontal is zero. The algebraic sum of all forces in the y-direction or vertical is zero. The algebraic sum of moment at any point O is zero. The three equilibrium conditions can solved up to three unknowns in the system. If the system involves more than three unknowns, it is called indeterminate. Indeterminate structures are beyond the scope of Engineering Mechanics.
Q.5 What is force system? A. Forces Systems When a mechanics problem or system has more than one force acting, it is known as a ‘force system’ or ‘system of force’. Q.6 What are the different types of supports, beams & loads? A. Types of support Supports are used to provide suitable reactions (Resistive force) to beam or any body. Following types of supports are used. Types of beam (a) Cantilever beam: A cantilever beam is fixed at one end and free at other end. (b) Simply supported beam: A simply supported beam is a type of beam that has pinned support at one end and roller support at the other end. Depending on the load applied, it undergoes shearing and bending. It is the one of the simplest structural elements in existence. (c) Overhanging beam: A overhanging beam is a beam that has one or both end portions extending beyond its supports. (d) Continuous beam: A continuous beam has more than two supports distributed throughout its length. (e) Fixed beam: As the name suggests, fixed beam is a type of beam whose both ends are fixed. Types of load
Value of UDL= load intensity (w) x length (L) acting at midpoint of CD Value of UVL= (1/2) x load intensity (w) x length (L) acting at CG of triangle formed (2L/3 from C or L/3 from D) Q.7 Draw stress strain diagram for Mild Steel. A. Relationship between Stress and Strain are derived on the basis of the elastic behaviour of material bodies. A standard mild steel specimen is subjected to a gradually increasing pull by Universal Testing Machine. The stress-strain curve obtained is as shown below. Elasticity and Elastic Limit Elasticity of a body is the property of the body by virtue of which the body regains its original size and shape when the deformation force is removed. Most materials are elastic in nature to a lesser or greater extend, even though perfectly elastic materials are very rare. The maximum stress upto which a material can exhibit the property of elasticity is called the elastic limit. If the deformation forces applied causes the stress in the material to exceed the elastic limit, there will be a permanent set in it. That is the body will not regain its original shape and size even after the removal of the deforming force completely. There will be some residual strain left in it. Yield stress When a specimen is loaded beyond the elastic limit the stress increases and reach a point at which the material starts yielding this stress is called yield stress. Ultimate stress Ultimate load is defined as maximum load which can be placed prior to the breaking of the specimen. Stress corresponding to the ultimate load is known as ultimate stress. Q.8 Derive the equation E = 2G (1+ μ). A. Consider a square element ABCD of side ‘a’ subjected to simple shear of intensity ‘τ’ as shown in figure.