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;

I_x – moment of inertia, meters ⁴;

Е – elastic modulus, pascal.

Расчет балки # 3.1

Calculation of a cantilever beam under moment load.

Boundary conditions:

R_L = 0 – support reaction at extremely left point;

M_L = 0 – bending moment at extremely left point;

θ_R = 0 – angle of rotation at extremely right point;

Y_R = 0 – deflection at extremely right point.

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:

R_L = 0 – support reaction at extremely left point;

θ_L = 0 – angle of rotation at extremely left point;

θ_R = 0 – angle of rotation at extremely right point;

Y_R = 0 – deflection at extremely right point.

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:

М_L = 0 – bending moment at extremely left point;

Y_L = 0 – deflection at extremely left point;

θ_R = 0 – angle of rotation at extremely right point;

Y_R = 0 – deflection at extremely right point.

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:

θ_L = 0 – angle of rotation at extremely left point;

Y_L = 0 – deflction at extremely left point;

θ_R = 0 – angle of rotation at extremely right point;

Y_R = 0 – deflection at extremely right point.

Ref 8 Table 8.1

Beam calculation # 3.5

Calculation of the beam with articulated supports under the action of bending moment.

Boundary conditions:

М_L = 0 – bending moment at extremely left point;

Y_L = 0 – deflection at extremely left point;

М_R = 0 – bending moment at extremely right point;

Y_R = 0 – deflection at extremely right point.

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:

R_L = 0 – support reaction at extremely left point;

θ_L = 0 – angle of rotation at extremely left point;

М_R = 0 – bending moment at extremely right point;

Y_R = 0 – deflection at extremely right point.

Ref 8 Table 8.1

Other calculators

– moments of inertia of sections

– beams with concentrated load

– torsion bar calculations

– round plates with linearly distributed load

– round plates with uniformly distributed pressure

– round plates with variable distributed pressure

– structural stability calculations

– contact stress calculations