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현재 위치

Cantilever beam, shear force calculation at any point, trapezoidal distribution load

작성자 Uploader : metalheart 작성일 Upload Date: 2019-10-29변경일 Update Date: 2019-12-29조회수 View : 982

When the trapezoidal distribution load acts on the cantilever beam as shown in the figure, the shear force SFx at any point x can be obtained as below.

The reaction force R at the point is

R = (1/2) (P1 + P2) * L

If P1 ≤ P2,

The linear equation of the load from point to x is

y = (P2-P1) * x / L + P1

If P1 ≥ P2,

y =-(P1-P2) * x / L + P1 = (P2-P1) * x / L + P1

Since the two linear equations are equal and P1 at x = 0,

∑P = (P1 + (P2-P1) * x / L + P1) * (x / 2) = (x / 2) * (2 * P1 + (P2-P1) * x / L)

Minus the distribution load up to x from the reaction force, then,

SFx = (P1 + P2) * L / 2-(x / 2) * (2 * P1 + (P2-P1) * x / L)

*** 참고문헌[References] ***

SFx = (P1+P2)*L/2 - (x/2)*(2*P1+(P2-P1)*x/L)

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현재 위치

Cantilever beam, shear force calculation at any point, trapezoidal distribution load

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