Beam calculation. Part III
In this part, the calculations of beams under action of a bending moment are performed. Calculations determine the deflection, the angle of rotation, and the bending moment at an arbitrary given point of the beam under various boundary conditions.
Initial data:
L – beam length, in millimeters;
a – coordinate of the load application point, millimeters;
X – coordinate of the solution point, millimeters;
T – bending moment, newtons×meter;
Ix – moment of inertia, meters 4;
Е – elastic modulus, pascal.
Расчет балки # 3.1
Calculation of a cantilever beam under moment load.
Boundary conditions:
RL = 0 – support reaction at extremely left point;
ML = 0 – bending moment at extremely left point;
θR = 0 – angle of rotation at extremely right point;
YR = 0 – deflection at extremely right point.
BENDING BEAM #1
Beam length L, mm
Distance A, mm
X coordinate, mm
Bending moment T, N*m
Section moment of inertia Iy, m4
Elastic modulus Е, Pa
Moment at point X, N*m
Angle of rotation at point X, deg
Deflection at point X, mm
Ref 8 Table 8.1
Beam calculation # 3.2
Calculation of the beam with a clamped end and a sliding support under the action of a bending moment.
Boundary conditions:
RL = 0 – support reaction at extremely left point;
θL = 0 – angle of rotation at extremely left point;
θR = 0 – angle of rotation at extremely right point;
YR = 0 – deflection at extremely right point.
BENDING BEAM #2
Beam length L, mm
Distance A, mm
X coordinate, mm
Moment T, N*m
Section moment of inertia Iy, m4
Elastic modulus Е, Pa
Moment at point X, N*m
Angle of rotation at point X, deg
Deflection at point X, mm
Ref 8 Table 8.1
Beam calculation # 3.3
Calculation of the beam with a clamped end and a hinged support under the action of a bending moment.
Boundary conditions:
МL = 0 – bending moment at extremely left point;
YL = 0 – deflection at extremely left point;
θR = 0 – angle of rotation at extremely right point;
YR = 0 – deflection at extremely right point.
BENDING BEAM #3
Beam length L, mm
Distance A, mm
X coordinate, mm
Moment T, N*m
Section moment of inertia Iy, m4
Elastic modulus Е, Pa
Moment at point X, N*m
Angle of rotation at point X, deg
Deflection at point X, mm
Ref 8 Table 8.1
Beam calculation # 3.4
Calculation of the beam with pinched ends under the action of a bending moment.
Boundary conditions:
θL = 0 – angle of rotation at extremely left point;
YL = 0 – deflction at extremely left point;
θR = 0 – angle of rotation at extremely right point;
YR = 0 – deflection at extremely right point.
BENDING BEAM #4
Beam length L, mm
Distance A, mm
X coordinate, mm
Moment T, N*m
Section moment of inertia Iy, m4
Elastic modulus Е, Pa
Moment at point X, N*m
Angle of rotation at point X, deg
Deflection at point X, mm
Ref 8 Table 8.1
Beam calculation # 3.5
Calculation of the beam with articulated supports under the action of bending moment.
Boundary conditions:
МL = 0 – bending moment at extremely left point;
YL = 0 – deflection at extremely left point;
МR = 0 – bending moment at extremely right point;
YR = 0 – deflection at extremely right point.
BENDING BEAM #5
Beam length L, mm
Distance A, mm
X coordinate, mm
Moment T, N*m
Section moment of inertia Iy, m4
Elastic modulus Е, Pa
Moment at point X, N*m
Angle of rotation at point X, deg
Deflection at point X, mm
Ref 8 Table 8.1
Beam calculation # 3.6
Calculation of the beam with articulated and sliding supports under the action of bending moment.
Boundary conditions:
RL = 0 – support reaction at extremely left point;
θL = 0 – angle of rotation at extremely left point;
МR = 0 – bending moment at extremely right point;
YR = 0 – deflection at extremely right point.
BENDING BEAM #6
Beam length L, mm
Distance A, mm
X coordinate, mm
Moment T, N*m
Section moment of inertia Iy, m4
Elastic modulus Е, Pa
Moment at point X, N*m
Angle of rotation at point X, deg
Deflection at point X, mm
Ref 8 Table 8.1
Other calculators
– moments of inertia of sections
– beams with concentrated load
– round plates with linearly distributed load
– round plates with uniformly distributed pressure
– round plates with variable distributed pressure
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