Shear and Moment Equations

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Presentation transcript:

Shear and Moment Equations 1 kip/ft 20 feet 10 kip V (kip) 10 -10 x V(x) = ? Symmetric beam – what are the reactions? How would you find an equation for shear, V(x)?

Shear and Moment Equations 1 kip/ft 20 feet 10 kip V (kip) 10 -10 x V(x) = mx + b

Shear and Moment Equations 1 kip/ft 20 feet 10 kip V (kip) 10 -10 x V(x) = -1kip/ft x + 10 kip Is it a coincidence that w and the slope have the same magnitude? (NO!)

1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50 How would you find an equation for Moment, M(x)? M (kip-ft) M(x) = ? x

1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50 How would you find an equation for Moment, M(x)? M (kip-ft) M(x) = ∫ V(x) x

1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50 How would you find an equation for Moment, M(x)? M (kip-ft) M(x) = ∫-1kip/ft x + 10 kip x

1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50 M(0) = 0 How would you find an equation for Moment, M(x)? M (kip-ft) 2 1 ft kip M(x)= - x + 10 kip x + C 2 x

1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50 M(0) = 0 M (kip-ft) 2 1 ft kip M(x)= - x + 10 kip x 2 x