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  3. 구조공학 Structural

Simple beam, distributed load, deflection at center

작성자 Uploader : metalheart 작성일 Upload Date: 2019-11-23변경일 Update Date: 2019-12-16조회수 View : 405

As shown in the figure, when the distributed load w (kN / m) is applied to a simple beam of length L (m), the deflection amount vmax (mm) at the center point of the beam is obtained as follows.

The amount of deflection vx (mm) at a distance x from the point A is

vx = -(w*x/(24*EI))*(L-x)(L^2+L*x-x^2)

If you apply MPa for the unit of E and the cm^4 for unit of I,

((kN/m)*m/(1000*kN/m^2*(0.01m)^4))*m^3 = 10^5*m

If the unit of vx is expressed in mm,

vx = -(w*x/(24*EI))*(L-x)*(L^2+L*x-x^2)*10^8

The amount of deflection at the center point is when x = L / 2 and the amount of deflection at this point is maximum.

vmax = -(w*(L/2)/(24*EI))*(L-L/2)*(L^2+L*L/2-(L/2)^2)*10^8

vmax = -(5/(384*EI))*w*L^4*10^8


*** 참고문헌[References] ***
vmax = -(5/(384*E*I))*w*L^4*10^8
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변수명 Variable 변수값 Value 변 수 설 명 Description of the variable


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