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When a distributed load is applied to beam, the location of the support point where the moment becomes zero at the center of the beam

ÀÛ¼ºÀÚ Uploader : milinae ÀÛ¼ºÀÏ Upload Date: 2023-05-23º¯°æÀÏ Update Date: 2023-05-23Á¶È¸¼ö View : 90

When the length of the beam is L (m), the length between the end of the beam and the support point is L1 (m), and the magnitude of the applied distributed load is w (kN/m), the length L1 (m) that makes the moment at the center of the beam is 0 can be calculated .

Reaction force at support

RA = RB = w*L/2

Moment at beam center

MC = RA*(L/2-L1) - w*(L/2)*(L/4) = 0

(w*L/2)*(L/2-L1) - (w/8)*L^2 = 0

(w/4)*(L*(L-2L1) - (1/2)*L^2) = 0

L^2 - 2L*L1 - (1/2)*L^2 = 0

2L*L1 = (1/2)L^2

L1 = (1/4)*L

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L1 = (1/4)*L
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