16-6.Distributed load such as double-point support beam
16-6. Distributed load such as double-point support beam
Symbol description and unit
Maximum deflection：(mm)
δmax(x=0)=1/24*ｗ*L
1
*(3*L
1
3
+6*L
1
2
*L
2
-L
2
3
)/(E*I)
δmax(x=0)=
δmax(x=L/2)=1/384*ｗ*L
2
2
*(5*L
2
2
-24*L
1
2
)/(E*I)
δmax(x=L/2)=
Maximum stress： (Kg/mm
2
)
σmax=M(x=L
1
)/Z=1/2*ｗ*L
1
2
/Z
σmax=
σmax=M(x=L/2)/Z=1/2*ｗ*L
2
*(L
1
/L-1/4)/Z
σmax=
E：Young's modulus(Kg/mm
2
)
Steel:21000
Stainless steel:19000
Aluminum:7000
cast iron:10000
I： Moment of inertia of area(mm
4
)
Z： Moment of inertia (mm
3
)
ｗ： Load B (Kg/mm)
L： Beam length (mm)
L
1
：Beam length to load position (mm)
L
2
：Beam length to load position (mm)
Reference: "Machine Design Handbook for Engineers" (Revised version by Saburo Kano) Applied Structural Mechanics Beam Calculation Table, page 142, refer to beams and columns.