Impact Loads Calculators

Impact on a Conical Bar

In this calculation, an impact of a movable element of mass m₁ on a conical bar of length L with a total own mass m is considered. The cross-sectional area of the bar changes from A₁ to A₂ linearly. At that, the movable element falls on the bar from a height H with initial speed W₀. For the calculation, the elastic modulus E of the bar should be specified. When calculating the impact, the equation of body motion is solved:

m₀Y'' = -P

After calculation of the reduced mass m₀ of the "bar-movable element" system, the stiffness K, maximum total deformation Y, impact load P, compressive stress σ in the bar and impact time T are determined. If the movable element impacts on the bar under the action of gravity, it is possible to take into account gravity upon impact.

Conical bar impact calculation

Conical bar under impact load

INITIAL DATA

m₁ - Mass of moving element;

A₁ - Area of the bar cross-section at the apex;

A₂ - Area of the bar cross-section at the base;

L - Bar length;

m - Total mass of the bar;

E - Young's modulus of the bar;

Н - Height of moving element above the bar;

W₀ - Initial speed of the moving element.

RESULTS DATA

Р - Maximum impact force;

σ - Maximum compressive stress on impact;

Y - Maximum total deformation on impact;

К - Bar stiffness;

Т - Impact time.

Metric Imperial

Mass (m₁)

Bar cross-section area (A₁)

Bar cross-section area (A₂)

Bar length (L)

Bar mass (m)

Young's modulus (Е)

Height (H)

Initial speed (W₀)

Gravity

Impact force (P)

Compressive stress (σ)

Bar deformation (Y)

Bar stiffness (К)

Impact time (Т)

BASIC FORMULAS

Bar stiffness:

K = E*(A₁ + A₂) / 2L;

Bar deformation:

Y = [(m1 + m*A₁ / (A₁ + A₂ + (A₁*A₁)^0,5))*W_0tot² / k]^1/2;

W_0tot - the total speed of the moving element and the bar at the moment of impact, calculated according to the law of conservation of momentum.

Impact force:

P = K*Y.

INITIAL DATA

m₁ - Mass of moving element;

A₁ - Area of the bar cross-section at the apex;

A₂ - Area of the bar cross-section at the base;

L - Bar length;

m - Total mass of the bar;

E - Young's modulus of the bar;

Н - Height of moving element above the bar;

W₀ - Initial speed of the moving element.

RESULTS DATA

Р - Maximum impact force;

σ - Maximum compressive stress on impact;

Y - Maximum total deformation on impact;

К - Bar 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)	-

OTHER CALCULATORS

AREA MOMENTS OF INERTIA

BEAM CALCULATORS

TORSION OF BARS

CIRCULAR FLAT PLATES

BUCKLING

ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

SHAFT CONNECTIONS

BEARINGS

DRIVES

FATIGUE

HEAT TRANSFER