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Simple beam, 3 concentrated loads, reaction force, shear force, bending moment

작성자 Uploader : milinae 작성일 Upload Date: 2023-07-15변경일 Update Date: 2023-07-16조회수 View : 457

Type1 Type2
As shown the figure, when the concentrated load P1, P2 and P3 (kN) at points L1, L2, and L3 (m) located from A are applied on a simple beam with a length of L (m), respectively, reaction force RA and RB (kN) at the supports A and B, shear force and bending moment can be calculated as follows. No Image
□ input data


1. Reaction forces

The moment at the support A is 0, so L1*P1+L2*P2+L3*P3 = L*RB


The sum of forces for vertical direction is 0, therefore,


2. Shear force

The shear force is constant in the AC, CD, DE, and EB sections and is as follows. (In the AC section, it is the same as RA.)
※ ↑↓ (+), ↓↑ (-)

- in the CD section


- in the DE section


- in the EB section


3. Bending moment

The moment of each section can be calculated by integrating the shear force.

The moment at A and B are 0.

- moment at the point C


- moment at the point D


- moment at the point E


- moment at B, for check


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