Beam Calculators

Beam with Fixed End and Sliding Support Under a Concentrated Load

In this calculation, a beam with one end fixed and the other guided, with a length L with a moment of inertia of cross section I_y is considered. The beam is subjected to a concentrated load F located at a distance a from the guided end.

As a result of calculations, a bending moment M at point X is determined. The bending moment takes extreme but opposite in sign values at the ends of the beam. Also, the inclination angle β equal to zero at the points of restraint, and the deflection Y, varying from zero at the fixed end to the maximum values at the sliding end of the beam are being determined.

For the calculation, the elastic modulus E of the beam should be specified.

Beam with fixed end and sliding support

Beam with fixed end and sliding support calculation

INITIAL DATA

L - Beam length;

a - Load point coordinate (distance from the left end of the beam to the load point);

X - Coordinate of the point at which the bending moment, slope and deflection of the beam are calculated (distance from the left end of the beam to the calculated point);

F - Concentrated load;

I_x - Moment of inertia of the cross-section;

Е - Young's modulus of the beam material.

RESULTS DATA

M - Bending moment at the point X;

β - Beam slope angle at the point X;

Y - Beam deflection at the point X.

Metric Imperial

Beam length (L)

Distance (a)

Point coordinate (X)

Load (F)

Moment of inertia (I_x)

Young's modulus (Е)

Bending moment (М)

Angle of slope (β)

Deflection (Y)

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BASIC FORMULAS

Bending moment, slope and deflection are determined by parametric equations depending on boundary conditions:

R₁ = 0 - Support reaction at the left end of the beam;
β₁ = 0 - Slope at the left end of the beam;
β₂ = 0 - Slope at the right end of the beam;
Y₂ = 0 - Deflection at the right end of the beam.

INITIAL DATA

L - Beam length;

a - Load point coordinate (distance from the left end of the beam to the load point);

X - Coordinate of the point at which the bending moment, slope and deflection of the beam are calculated (distance from the left end of the beam to the calculated point);

F - Concentrated load;

I_x - Moment of inertia of the cross-section;

Е - Young's modulus of the beam material.

RESULTS DATA

M - Bending moment at the point X;

β - Beam slope angle at the point X;

Y - Beam deflection at the point X.

MATERIALS PROPERTIES

Material	Young’s modulus Pa (psi)	Poisson’s ratio
Steel	1.86÷2.1×10¹¹ (2.7÷3.05×10⁷)	0.25÷0.33
Cast iron	0.78÷1.47×10¹¹ (1.1÷2.1×10⁷)	0.23÷0.27
Copper	1.0÷1.3×10¹¹ (1.45÷1.9×10⁷)	0.34
Tin bronze	0.74÷1.22×10¹¹ (1.1÷1.8×10⁷)	0.32÷0.35
Brass	0.98÷1.08×10¹¹ (1.4÷1.6×10⁷)	0.32÷0.34
Aluminum alloy	0.7×10¹¹ (1.0×10⁷)	0.33
Magnesium alloy	0.4÷0.44×10¹¹ (5.8÷6.4×10⁶)	0.34
Nickel	2.5×10¹¹ (3.6×10⁷)	0.33
Titanium	1.16×10¹¹ (1.7×10⁷)	0.32
Lead	0.15÷0.2×10¹¹ (2.2÷2.9×10⁶)	0.42
Zinc	0.78×10¹¹ (1.1×10⁷)	0.27
Glass	4.9÷5.9×10¹⁰ (7.1÷8.5×10⁶)	0.24÷0.27
Concrete	1.48÷2.25×10¹⁰ (2.1÷3.3×10⁶)	0.16÷0.18
Wood (along the grain)	8.8÷15.7×10¹⁰ (12.8÷22.8×10⁶)	-
Wood (across the grain)	3.9÷9.8×10¹⁰ (5.7÷14.2×10⁶)	-
Nylon	1.03×10¹⁰ (1.5×10⁶)	-

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