SS - Notes Flashcards
The resultant is directed away form the starting point
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The resultant is concurrent with the original forces (their lines of action pass through a common point)
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Equilibrium:
- The summation of all the horizontal forces acting on the body must equal zero.
- The summation of all the vertical forces acting on the body must equal zero.
- The summation of all the moments acting on the body must equal zero.
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The order in which the forces are drawn in the force polygon makes no difference; the resultant will be the same in both magnitude and direction regardless of the order followed.
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The value of the moment (M) at the supports of a simple beam is zero.
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Positive values of shear are shown above the base line and negative values below the base line.
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The value of shear changes abruptly at concentrated loads and reactions and is indicated by a vertical line
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Where the value of shear is constant, the shear diagram is horizontal.
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The two points on the shear diagram that are of greatest interest in structural design are: (1) where the shear has the maximum value, and (2) where the shear passes through zero; that is, where it changes from positive to negative or vice versa.
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The value of shear changes at a uniform rate at uniformly distributed loads, and therefore the corresponding shear diagram is a line of constant slope.
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Positive values of moment are shown above the base line and negative values, if any, below the base line.
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The slope of the moment diagram is equal to the value of the shear diagram at the same point on the beam. Thus, where the shear is constant, the shear diagram is horizontal and the moment diagram is a line of constant slope. At concentrated loads, the shear changes abruptly, and therefore the slope of the moment diagram changes abruptly.
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The bending moment is maximum where the shear passes through zero.
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The change of moment between any two points is equal to the area of the shear diagram between those two points.
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Simple beams are bent concave upward; the upper beam fibers are stressed in compression, while the lower fibers are in tension. This is called positive moment. simple beams supporting downward vertical loads have positive moment across the entire span.
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Cantilever beams are bent concave downward; the upper beam fibers are stressed in tension, while the lower fibers are in compression. This is called negative moment. Cantilever beams resisting downward vertical loads have negative moment throughout their length.
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