﻿ Impact loads Calculators | Straight bar

## Impact on Straight Bar

The dynamic phenomena are characterized by the presence of inertial forces during the movement of structural elements, comparable in value with the external loads on the system, as well as such time-varying characteristics as speed, acceleration, loads and deformations.

The analysis of dynamic systems is always more complex than the static calculations. This is due to the dependence of external influences on the reaction of the system, and the properties of the system itself on the characteristics of movement. Difficulties also arise as a result of the fact that it is often impossible to determine the most essential properties of the system in advance, when constructing a mathematical model.

In mechanics, the impact loads during operation are often decisive, or have a periodic nature, or are the result of accidents. The main sign of the impact loads is the short duration of the impact on the structure.

During the impact, a sharp change in the velocities of the system points occurs, and short-term great forces are generated. From the point of view of mechanics, the impact energy provides the possibility of a multiple increase in the load acting on the structure at small displacements.

The condition for the impact occurrence is the presence of a relative velocity of the interacting bodies, as a result of which a momentum and energy exchange occurs. At that, local deformations and stresses arise, propagating by a wave with a sonic or supersonic speed.

Currently, the problems of dynamics are solved mainly by the FEA. Using our calculators, it is possible to calculate the impact loads, displacements and collision times for bars, beams and the most common general viscoelastic model.

In this calculation, the impact of a movable element with a mass m1 on a bar of length L, cross-sectional area A and total own mass m is considered. 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 "bar-movable element" system, the stiffness K, maximum total deformation X, 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.  ### INITIAL DATA

m1 - Mass of moving element;

A - Area of the bar cross-section;

L - Bar length;

m - Total mass of the bar;

E - Young's modulus;

Н - Height of the 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.

Mass (m1)

Bar cross-section area (A)

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*A / L;

Bar deformation:

Y = [(m1 + m/3)*W0tot2 / k]1/2;

W0tot - 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;

A - Area of the bar cross-section;

L - Bar length;

m - Total mass of the bar;

E - Young's modulus;

Н - Height of the 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) -