# Beam calculation. Part II

Below, we performed online calculations of beams under variable distributed load. The calculations determine the deflection, angle of rotation, and bending moment at an arbitrary given point of the beam under various boundary conditions.

### Initial data:

L – beam length, millimeters;

a – coordinate of the start point of the distributed load, millimeters;

X – coordinate of the solution point, millimeters;

q_{a} – distributed load value at point “a”, newtons / meter;

q_{l} – distributed load value at extremely right point, in newtons / meter;

I_{x} – moment of inertia of the section, in meters ^{4};

Е – elastic modulus of the material of the beam, in pascals.

## Beam calculation # 1.2

Calculation of cantilever beam under distributed 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.

BEAM UNDER DISTRIBUTED LOAD #1

Beam length L, mm

Distance A, mm

X coordinate, mm

Specific load q_{l}, N/m

Specific load q_{a}, N/m

Section moment of inertia I_{y}, m^{4}

Elastic modulus Е, Па

Moment at point X, N*m

Angle of rotation at point X, deg

Deflection at point X, mm

©Copyright Caetec 2020

*Ref 8 Table 8.1*

## Beam calculation # 2.2

Calculation of the beam with a clamped end and a sliding support under distributed load.

#### 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.

BEAM UNDER DISTRIBUTED LOAD #2

Beam length L, mm

Distance A, mm

X coordinate, mm

Specific load q_{l}, N/m

Specific load q_{a}, N/m

Section moment of inertia I_{y}, m^{4}

Elastic modulus Е, Pa

Moment at point X, N*m

Angle of rotation at point X, deg

Deflection at point X, mm

©Copyright Caetec 2020

*Ref 8 Table 8.1*

## Beam calculation # 3.2

Calculation of the beam with a clamped end and articulated support under distributed load.

#### 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.

BEAM UNDER DISTRIBUTED LOAD #3

Beam length L, mm

Distance A, mm

X coordinate, mm

Specific load q_{l}, N/m

Specific load q_{a}, N/m

Section moment of inertia I_{y}, m^{4}

Elastic modulus Е, Pa

Moment at point X, N*m

Angle of rotation at point X, deg

Deflection at point X, mm

©Copyright Caetec 2020

*Ref 8 Table 8.1*

## Beam calculation #4.2

Calculation of the beam with pinched ends under distributed load.

#### Boundary conditions:

θ_{L} = 0 – angle of rotation 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.

BEAM UNDER DISTRIBUTED LOAD #4

Beam length L, mm

Distance A, mm

X coordinate, mm

Specific load q_{l}, N/m

Specific load q_{a}, N/m

Section moment of inertia I_{y}, m^{4}

Elastic modulus Е, Pa

Moment at point X, N*m

Angle of rotation at point X, deg

Deflection at point X, mm

©Copyright Caetec 2020

*Ref 8 Table 8.1*

## Beam calculation # 5.2

Calculation of the beam with articulated supports under distributed load.

#### 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.

BEAM UNDER DISTRIBUTED LOAD #5

Beam length L, mm

Distance A, mm

X coordinate, mm

Specific load q_{l}, N/m

Specific load q_{a}, N/m

Section moment of inertia I_{y}, м^{4}

Elastic modulus Е, Pa

Moment at point X, N*m

Angle of rotation at point X, deg

Deflection at point X, mm

©Copyright Caetec 2020

*Ref 8 Table 8.1*

## Beam calculation # 6.2

Calculation of the beam with articulated and sliding supports under distributed load.

#### 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.

BEAM UNDER DISTRIBUTED LOAD #6

Beam length L, mm

Distance A, mm

X coordinate, mm

Specific load q_{l}, N/m

Specific load q_{a}, N/m

Section moment of inertia I_{y}, m^{4}

Elastic modulus Е, Pa

Moment at point X, N*m

Angle of rotation at point X, deg

Deflection at point X, mm

©Copyright Caetec 2020

*Ref 8 Table 8.1*

## Other calculators

– beams with concentrated load

– round plates with linearly distributed load

– round plates with uniformly distributed pressure

– round plates with variable pressure

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