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
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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.
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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
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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
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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
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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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This note was uploaded on 06/18/2009 for the course CE xxx taught by Professor Tuken during the Spring '09 term at Middle East Technical University.

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

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