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chapter3 (statics of rigid bodies)

# chapter3 (statics of rigid bodies) - CHAPTER THREE STATICS...

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CHAPTER THREE STATICS OF RIGID BODIES

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3.1 INTRODUCTION A rigid body is one which does not suffer deformation. It can be continuous connected members. F 2 F 3 F 1 P 2 P 1 F 3 F 1 F 2 Continuous Member Connected Members
INTRODUCTION CONTD. The forces acting on rigid bodies can be internal or external. F 1 , F 2 and F 3 which are applied by an external force on the rigid body are called external forces. P 1 and P 2 which are forces internal to the rigid body are called internal forces.

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INTRODUCTION CONCLUDED. The external forces are completely responsible for the bulk motion of the rigid body. As far as this bulk motion is concerned, the internal forces are in equilibrium.
3.2 PRINCIPLE OF TRANSMISSIVITY OF FORCES External forces generally cause translation i.e. linear motion and/or rotation (motion about a pivot) of the rigid body.

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PRINCIPLE OF TRANSMISSIVITY OF FORCES Principle of transmissivity states that the condition of rest or motion of a rigid body is unaffected if a force, F acting on a point A is moved to act at a new point, B provided that the point B lies on the same line of action of that force. A B F F
3.3 CROSS OR VECTOR PRODUCT OF TWO VECTORS The moment of a force will be formulated using Cartesian vectors in the next section. It is necessary to first expand our knowledge of vector algebra and introduce the cross-product method of vector multiplication.

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Cross Products of ForcesP and Q The cross product of two vectors , P and Q yields the vector, V which is written: V = P x Q ( i.e V = P cross Q). 3.3.1 Magnitude: The magnitude of V is the product of the magnitudes of P and Q and sine of the angle θ between their tails ( 0 < θ < 180 o ). Thus : V = P Q Sin θ
3.3.2 Direction Vector, V has a direction that is perpendicular to the plane containing P and Q such that the direction of V is specified by the right hand rule i.e. curling the fingers of the right hand from vector P (cross) to vector Q , the thumb then points in the direction of V .

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Direction of Cross Product The sense of V is such that a person located at the tip of V will observe as counterclockwise the rotation through θ that brings the vector P in line with vector Q . Knowing the magnitude and direction of V: V = P x Q = (P Q sin θ ) λ v Where: the scalar PQ sin θ defines the magnitude of V and the unit vector, λ v defines the direction of V . V = P x Q V Q PQ sin θ = V θ θ Q P P
3.3.3. Laws of Operation 1 . The cummutative law does not apply i.e. P x Q Q x P Rather: P x Q = - Q x P 2. Multiplication by a scalar a ( P x Q ) = (a P ) x Q = P x ( a Q ) = ( P x Q ) a 3 . The distributive law: P x ( Q + S ) = ( P x Q ) + ( P x S ) 4 . The associative property does not apply to vector products ( P x Q ) x S P ( Q x S )

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Cartesian (Rectangular) Vector Formulation y j x k = (i x j) i z To find i x j, the magnitude of the resultant is:
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chapter3 (statics of rigid bodies) - CHAPTER THREE STATICS...

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