User:Stephen Mckelvey/sandbox

Overview

The dynamic lift factor (DLF), also known as the design dynamic factor, is a critical parameter in the crane design and operation. It accounts for the dynamic effects that can increase the load on a crane's structure and components during lifting operations. These effects include:

• Hoisting acceleration and deceleration of the load, which is a significant factor;
• Crane movement such as slewing or luffing;
• Load swinging;
• Wind forces acting on the crane, the load and the rigging; and
• Operator error or other unexpected events.

The DLF for a new crane design can be determined with analytical calculations and mathematical models following the relevant design specifications. If available, data from previous tests of similar crane types can be used to estimate the DLF. More sophisticated methods, such as finite element analysis or other simulation techniques, may also be used to model the crane's behavior under various loading conditions, as deemed appropriate by the designer or certifying authority.To verify the actual DLF, control load tests can be conducted on the completed crane using instrumentation such as load cells, accelerometers, and strain gauges. This process is usually part of the crane's type approval.

In offshore lifting, where the crane and/or lifted object are on a floating vessel, the DLF is higher compared to onshore lifts because of the additional movement caused by wave action. This motion introduces additional acceleration forces and necessitates increased hoisting and lowering speeds to minimize the risk of repeated collisions when the load is near the deck. Additionally, the DLF increases further when lifting objects that are underwater or going through the splash zone. The wind speeds tend to be higher than onshore as well.

Though actual DLF values are determined through crane tests under representative operational conditions, design specifications can be used for guidance. The values vary according to the specification, which reflects the type of crane and its usage. Here are some example typical values:

• Jib cranes typically have a lower DLF (${\textstyle \psi \approx 1.3}$) compared to traveling gantry cranes ($\psi \approx 1.6$) because they are stiffer;
• For grab cranes, the DLF can increase by 20% to 30% reflecting the shock loads caused by the release of the lifted material; and
• The DLF generally decreases as the mass of the lifted object increases, as cranes tend to operate at lower velocities with heavier loads to ensure safety and stability. For offshore lifts, the DLF typically decreases from 1.3 at 100 tonnes to 1.1 at 2500 tonnes.

Formulas

The methods for determining the DLF vary in the different crane specifications. The following formulas a examples from one specification.

The working load (suspended load) is the total weight that a crane is designed to safely lift under normal operating conditions. It is

$W=g\cdot (m_{wll}+m_{a})$

where

${\textstyle W}$ is the working load,

${\textstyle g}$ is the acceleration of gravity,

${\textstyle m_{wll}}$ is the maximum lifted mass, which is also called the crane working load limit (WLL) or safe working load (SWL), and

${\textstyle m_{a}}$ is the mass of lifting appliances or parts of the crane that move with the lifted mass.

The DLF is then used as a multiplier to determine the force applied to the crane structure and components

$F_{d}=\psi \ \cdot W$

where

${\textstyle F_{d}}$ is the design force, and

${\textstyle \psi }$ is the DLF.

The DLF can then be calculated using

$\psi =1+V_{R}\cdot {\sqrt {C/(W\cdot g)}}$

where

${\textstyle V_{R}}$ is relative velocity between lifted object and hook at the time of pick-up, and

${\textstyle C}$ is the stiffness of the crane system at the hook.

The relative velocity is dependent on the crane's operational requirements and the system stiffness at the hook can be determined by calculation or load deflection tests.

Deviation of engineering stress from true stress

When a uniaxial compressive load is applied to an object it will become shorter and spread laterally so its original cross sectional area (${\textstyle A_{o}}$) increases to the loaded area (${\textstyle A}$) . Thus the true stress (${\acute {\sigma }}=F/A$) deviates from engineering stress ($\sigma _{e}=F/A_{o}$). Tests that measure the engineering stress at the point of failure in a material are often sufficient for many routine applications, such as quality control in concrete production. However, determining the true stress in materials under compressive loads is important for research focused on the properties on new materials and their processing.

The geometry of test specimens and friction can significantly influence the results of compressive stress tests. Friction at the contact points between the testing machine and the specimen can restrict the lateral expansion at its ends (also known as 'barreling') leading to non-uniform stress distribution. This is discussed in section on contact with friction.

Frictionless contact

With a compressive load on a test specimen it will become shorter and spread laterally so its cross sectional area increases and the true compressive stress is$${\acute {\sigma }}=F/A$$and the engineering stress is$${\sigma _{e}}=F/A_{o}$$The cross sectional area (${\textstyle A}$) and consequently the stress ( ${\textstyle {\acute {\sigma }}}$) are uniform along the length of the specimen because there are no external lateral constraints. This condition represents an ideal test condition. For all practical purposes the volume of a high bulk modulus material (e.g. solid metals) is not changed by uniaxial compression . So$$Al=A_{o}l_{o}$$Using the strain equation from above$$A=A_{o}/(1+\epsilon _{e})$$and$${\acute {\sigma }}=\sigma _{e}(1+\epsilon _{e})$$Note that compressive strain is negative, so the true stress (${\acute {\sigma }}$ ) is less than the engineering stress (${\textstyle \sigma _{e}}$). The true strain (${\acute {\epsilon }}$) can be used in these formulas instead of engineering strain (${\textstyle \epsilon _{e}}$) when the deformation is large.

Contact with friction

As the load is applied, friction at the interface between the specimen and the test machine restricts the lateral expansion at its ends. This has two effects:

• It can cause non-uniform stress distribution across the specimen, with higher stress at the centre and lower stress at the edges, which affects the accuracy of the result.

• It causes a barreling effect (bulging at the centre) in ductile materials. This changes the specimen’s geometry and affects its load-bearing capacity, leading to a higher apparent compressive strength.

Various methods can be used to reduce the friction according to the application:

• Applying a suitable lubricant, such as MoS2, oil or grease; however, care must be taken not to affect the material properties with the lubricant used.

• Use of PTFE or other low-friction sheets between the test machine and specimen.
• A spherical or self-aligning test fixture, which can minimize friction by applying the load more evenly across the specimen's surface.

Three methods can be used to compensate for the effects of friction on the test result:

1. Correction formulas
2. Geometric extrapolation
3. Finite element analysis

Correction formulas

Round test specimens made from ductile materials with a high bulk modulus, such as metals, tend to form a barrel shape under axial compressive loading due to frictional contact at the ends. For this case the equivalent true compressive stress for this condition can be calculated using$${\acute {\sigma }}=C\sigma _{a}$$where

$C={(1-2R/d_{2})\ln(1-d_{2})/(2R))}^{-1}$

$R=(l^{2}+(d_{2}-d_{1})^{2})/(4(d_{2}-d_{1}))$

$\sigma _{a}=4F/(\pi d_{2}^{2})$

$l$ is the loaded length of the test specimen,

$d_{1}$is the loaded diameter of the test specimen at its ends, and

$d_{2}$is the maximum loaded diameter of the test specimen.

Note that if there is frictionless contact between the ends of the specimen and the test machine, the bulge radius becomes infinite (${\textstyle R=\infty }$) and ${\textstyle C=1}$ . In this case, the formulas yield the same result as ${\textstyle {\acute {\sigma }}=\sigma _{e}(1+\epsilon _{e})}$ because ${\textstyle \sigma _{a}}$ changes according to the ratio $(d_{o}/d_{2})^{2}$.

The parameters (${\textstyle F,d_{1},d_{2},l}$) obtained from a test result can be used with these formulas to calculate the equivalent true stress ${\textstyle {\acute {\sigma }}}$ at failure.

Specimen shape effect

The graph of specimen shape effect shows how the ratio of true stress to engineering stress (σ´/σ_e) varies with the aspect ratio of the test specimen (${\textstyle d_{o}/l_{o}}$). The curves were calculated using the formulas provided above, based on the specific values presented in the table for specimen shape effect calculations. For the curves where end restraint is applied to the specimens, they are assumed to be fully laterally restrained, meaning that the coefficient of friction at the contact points between the specimen and the testing machine is greater than or equal to one (μ ⩾ 1). As shown in the graph, as the relative length of the specimen increases (${\textstyle d_{o}/l_{o}\rightarrow 0}$), the ratio of true to engineering stress (${\acute {\sigma }}/\sigma _{e}$) approaches the value corresponding to frictionless contact between the specimen and the machine, which is the ideal test condition.

Specimen shape effect calculations

	Frictionless	Laterally Constrained
Constant volume	$\pi l_{o}d_{o}^{2}/4=\pi l(d_{2}^{2}+d_{1}^{2})/12$
Equal diameters	$d_{1}=d_{2}$	$d_{o}=d_{1}$
Solve for $d_{2}$	$\pi l_{o}d_{o}^{2}/4=\pi l(d_{2}^{2}+d_{2}^{2})/12$	$\pi l_{o}d_{o}^{2}/4=\pi l(d_{2}^{2}+d_{o}^{2})/12$
	$d_{2}=d_{o}{\sqrt {l_{o}/l}}$	$d_{2}=3d_{o}{\sqrt {(3l_{o}/l-1)/18}}$
Equivalent stress ratio	${\acute {\sigma }}/\sigma _{a}=1$	${\acute {\sigma }}/\sigma _{a}=C$
Engineering stress	$\sigma _{e}=4F/\pi d_{o}^{2}$
Average stress	$\sigma _{a}=4F/\pi d_{2}^{2}$
Average stress ratio	$\sigma _{a}/\sigma _{e}=(d_{o}/d_{2})^{2}$
True strain	${\acute {\epsilon }}=\ln(l/l_{o})$

Geometric extrapolation

As demonstrated in the section on correction formulas, as the length of test specimens increases and their aspect ratio approaches zero ($d_{o}/l_{o}\longrightarrow 0$), the compressive stress (σ) approaches the true value (σ′). However, conducting tests with excessively long specimens is impractical, as they would fail by buckling before reaching the material's true compressive strength. To overcome this, a series of tests can be conducted using specimens with varying aspect ratios, and the true compressive strength can then be determined through extrapolation.

Test Methods

Laboratory

Common Applications:

   Concrete Testing: To ensure the material meets required strength specifications for construction.

   Metal and Alloy Testing: For quality control in manufacturing, especially for components subject to high compressive forces.

   Ceramics and Plastics: To test the durability of materials used in packaging, automotive, and aerospace industries.

This type of testing machine is crucial in quality control, research, and development, ensuring materials meet safety and performance standards.

There are a number of standards with industry specific recommendations for specimen preparation, conduct of the tests and analysis of the results. Commonly used standards are:

• ASTM E9-89A, Standard Test Methods of Compression Testing of Metallic Materials at Room Temperature
• ASTM D575-91 Standard Test Methods for Rubber Properties in Compression
• ASTM D3410 Compression of Composites

Most commonly cylindrical specimens are used: either prepared specifically for the test or cut from an existing material or structure.