Impact Load on a Simply Supported Beam | Online Calculator

Impact Loads Calculators







Impact on a Beam with Simply Supported Ends

In this calculation, an impact of a movable element of mass m1 on a beam of length L, total own mass m and moment of inertia of a cross-section Ix is considered. At that, the movable element falls on the beam from a height H with initial speed W0. For the calculation, the elastic modulus E of the beam should be specified. The ends of the beam are simply supported. When calculating the impact, the equation of body motion is solved:

m0Y'' = -P

After calculation of the reduced mass m0 of the "beam-movable element" system, the stiffness K, maximum total deformation Y, impact load P and impact time T are determined in calculated point, which is characterized by the coordinate a. If the movable element impacts on the beam under the action of gravity, it is possible to take into account gravity upon impact.

Calculation of impact on a beam with simply supported ends
Beam with simply supported ends under impact load

INITIAL DATA

m1 - Mass of moving element;


Ix - Moment of inertia of the beam cross-section;


L - Beam length;


a - Distance from end of the beam to point of impact;


m - Total mass of the the beam;


E - Young's modulus;


Н - Height of the moving element above the beam;


W0 - Initial speed of the moving element.

RESULTS DATA

Р - Maximum impact force;


Y - Maximum total deformation on impact;


К - Beam stiffness;


Т - Impact time.

Mass (m1)

Moment of inertia (Ix)

Beam length (L)

Distance to impact point (a)

Beam mass (m)

Young's modulus (Е)

Height (H)

Initial speed (W0)

Gravity

Impact force (P)

Beam deformation (Y)

Beam stiffness (К)

Impact time (Т)

BASIC FORMULAS

Beam deformation:

Y = [(m1 + ([2 + 4*(a/L) - (a/L)2 - 6(a/L)3 + 3(a/L)4] / [105(a/L)2*(1 - a/L)2)])*m)*W12 / K]1/2;

W1 - the total speed of the moving element and the beam at the moment of impact.

Impact force:

P = K*Y.

INITIAL DATA

m1 - Mass of moving element;


Ix - Moment of inertia of the beam cross-section;


L - Beam length;


a - Distance from end of the beam to point of impact;


m - Total mass of the the beam;


E - Young's modulus;


Н - Height of the moving element above the beam;


W0 - Initial speed of the moving element.

RESULTS DATA

Р - Maximum impact force;


Y - Maximum total deformation on impact;


К - Beam stiffness;


Т - Impact time.

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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