Chapter 15 — Weight Measurement ⚖️

Big idea: why measure weight?

Weight is often used in industrial processes when other quantity measurements, such as level measurement, are not accurate enough. For example, if a plant needs to add an exact amount of reagent into a reaction vessel, measuring the weight of the material can be more reliable than measuring how high the liquid level is.

Older systems used mechanical weighbridges with levers, counterweights, and springs. Modern industrial systems usually use load cells, which are based on strain gauges. The chapter explains how strain gauges work, how they are connected electrically, how load cells are built, and how they should be installed.

15.1 Resistance Effects 🔌

This section explains the physics behind strain gauges.

Electrical resistance of a wire

The resistance of a wire depends on three things:

R_0 = \rho \frac{L_0}{A_0}

Where:

So, a wire has higher resistance if it is longer, and lower resistance if it is thicker.

What happens when the wire is stretched?

When a wire is stretched:

• its length increases
• its cross-sectional area decreases
• its resistance increases

This is the key principle behind strain gauges.

The chapter simplifies the relationship to:

\frac{\delta R}{R_0} \approx 2 \frac{\delta L}{L_0}

This means:

The fractional change in resistance is proportional to the fractional change in length.

The fractional change in length is called strain.

Gauge factor

The value 2 in the equation is called the gauge factor.

A gauge factor tells you how sensitive a strain gauge is. If the gauge factor is high, a small stretch produces a larger resistance change.

For ordinary metal foil strain gauges, the gauge factor is often around 2.

Connecting strain to force

The chapter then links this to Hooke’s law:

\frac{F}{A} = E \frac{\delta L}{L_0}

This says:

Stress is proportional to strain.

Where:

So the full logic is:

Force applied → material stretches → strain occurs → resistance changes → force can be measured

That is the entire foundation of strain-gauge-based weight measurement.

Temperature problem 🌡️

Resistance does not only change because of strain. It also changes with temperature:

R = R_0(1 + a(T - T_0))

This matters because if temperature changes, the instrument might falsely interpret that as a change in weight.

So the system needs temperature compensation, which becomes important later when the chapter introduces Wheatstone bridges.

15.2 Strain Gauges 🧩

A strain gauge is a device that converts mechanical strain into a measurable electrical resistance change.

What does a strain gauge look like?

The most common type is a foil strain gauge. It consists of a very thin metal foil etched onto a plastic film.

The diagram on page 2 shows a foil strain gauge with:

• etched constantan foil
• solder pads
• plastic backing
• alignment marks
• a folded zig-zag pattern

The folded pattern lets a long piece of foil fit into a small area, like packing a long road into a tiny map. This makes the gauge small but still sensitive.

Why is the foil folded?

Sensitivity depends partly on the geometry. A good strain gauge needs:

• relatively high resistance
• enough length of foil
• very thin foil

The foil is commonly only about 5 μm thick, which is extremely thin.

By folding the foil, the gauge can have a long effective length while still being physically small.

Direction matters: principal axis 🎯

The diagram on page 2 also shows that the strain gauge has a principal axis.

The gauge is most sensitive to stretching along this main direction. It is much less sensitive to strain across the other direction.

This makes strain gauges directional.

So when installing a strain gauge, it must be aligned carefully with the direction of the force being measured.

Common materials

The chapter says the common material is constantan, an alloy made of:

• 55% copper
• 45% nickel

Constantan is useful because it has a gauge factor of about 2, close to the ideal theoretical value.

Other alloys can have gauge factors from 2 to 10, but they are usually more temperature-sensitive.

There are also semiconductor strain gauges with much higher gauge factors, around 50 to 200, meaning they are far more sensitive. However, their response is nonlinear, which makes calibration and interpretation harder.

How strain gauges measure force

A strain gauge is bonded onto a rigid member. When the member stretches or compresses, the gauge stretches or compresses with it.

Example:

1. A force is applied to a metal beam.
2. The beam slightly deforms.
3. The strain gauge bonded to the beam also deforms.
4. The gauge’s resistance changes.
5. The resistance change is measured.
6. The force is calculated through calibration.

The important point is that the strain gauge does not directly measure weight. It measures strain, and strain is then related to force.

Bonding is critical 🧪

The gauge must be firmly bonded to the surface. If the bond is poor, the strain in the metal member will not be properly transferred to the gauge.

The chapter mentions that proprietary cements or adhesives are used. For acrylic film gauges, methyl methacrylate-based adhesive, such as superglue, can be used because it dissolves the acrylic slightly and forms a seamless bond.

A poor bond gives poor measurement.

Insulation and moisture protection 💧

The strain gauge must not short-circuit.

There are two big risks:

1. Shorting to the metal surface

Since the gauge is bonded onto a metallic member, it must be electrically insulated from that surface. Usually, the plastic film and adhesive provide enough insulation.

2. Moisture between foil tracks

The folded foil has many closely spaced tracks. Moisture can create unwanted electrical paths between them, causing short circuits.

Therefore, strain gauges are often hermetically sealed to protect them from moisture.

Wheatstone Bridge Measurement 🌉

The chapter explains that strain gauge resistance is usually measured using a Wheatstone bridge circuit.

This is shown on page 3.

Why use a Wheatstone bridge?

The resistance change in a strain gauge is very small. A Wheatstone bridge is useful because it can detect tiny changes in resistance accurately.

The bridge converts a small resistance change into a measurable voltage output.

Active and dummy gauges

To deal with temperature effects, the system uses two gauges:

Both gauges are placed close together, so they experience the same temperature.

The active gauge changes resistance because of both strain and temperature. The dummy gauge changes resistance only because of temperature.

Because they are placed on opposite sides of the bridge, the temperature effects cancel out.

That means the output mainly represents strain, not temperature.

Output signal

The bridge output voltage is approximately proportional to strain.

The chapter says the excitation voltage is typically a chopped 10 V DC supply, producing an output of around 0–20 mV.

That is a tiny signal, so it needs signal conditioning. After conditioning, the signal may become:

• a 4–20 mA analogue signal, or
• a digital serial signal

These are easier to transmit and use in industrial control systems.

15.3 Load Cells 🏗️

A load cell is a rugged industrial device that uses strain gauges to measure force or weight.

Strain gauges alone are delicate. In a real plant environment, they need protection. Load cells provide this protection and allow the strain gauges to be placed safely in the load path.

What does a load cell do?

A load cell converts force into an electrical signal.

The logic is:

Weight → force on load cell → deformation → strain gauge resistance change → electrical output

Load cell capacity

The chapter says load cells can measure from very small loads to enormous loads:

• individually down to about 25 g
• in combination up to about 5000 tonnes

So the same basic principle can be used for small laboratory-scale weighing and huge industrial vessels.

Accuracy and limitations

Properly calibrated load cells can be very accurate:

However, there is an important warning:

The zero setting can drift.

This means load cells are better for measuring changes in weight than absolute weight unless regularly zeroed or calibrated.

Tare weight and live weight

The chapter gives design guidance:

For good specification:

• tare weight should be about 5–50% of full range
• live weight should be about 20–75% of full range
• batching resolution should not be less than 0.02% of full range

This matters because choosing a load cell with too large a range gives poor resolution. Choosing one with too small a range risks overload.

Types of Load Cells

1. Canister load cell 🛢️

The canister type is used for loads up to about 250 tonnes.

The diagram on page 3 shows a canister load cell with a central load-bearing column.

It has four strain gauges:

• one pair mounted horizontally
• one pair mounted vertically

When a load is applied, the central column compresses vertically and expands laterally. This relationship is connected to Poisson’s law.

The four gauges are arranged in a bridge circuit, shown on page 4.

Why use four gauges?

A four-gauge bridge gives better sensitivity and built-in temperature compensation.

Because the gauges are arranged so that some experience compression and others experience tension, the output becomes stronger and more reliable.

The bridge also helps cancel temperature effects.

2. Shear beam load cell 🧱

The shear beam type is widely used for loads up to about 25 tonnes.

It works like a cantilever arm. When load is applied, it produces shear forces.

The cell is made by machining a central web into a steel block. This web has a high and nearly uniform shear strain.

The chapter says shear strain is highest at 45° to the vertical.

Therefore, the strain gauges are mounted at:

• 45°
• 135°

This is shown in the diagram on page 4.

Why shear beam cells are useful

Shear beam load cells tolerate some imperfections better than other designs.

They are:

• tolerant of variation in vertical load position
• fairly insensitive to bending stresses
• able to tolerate some sideways loads and torques

Because of this, shear beam load cells are especially suitable for agitated vessels, where mixers can create vibration, torque, and uneven loading.

15.4 Installation 🛠️

This section explains how load cells should be installed in real process plants.

Good installation is just as important as choosing the right load cell. A high-quality load cell can still give bad readings if installed poorly.

Compression mounting

For weighing process vessels, load cells are usually used under compression.

That means the vessel sits on the load cells, pressing downward.

The diagrams on page 4 show examples such as:

• a three-legged tank sitting on canister load cells
• a suspended mid-floor arrangement using shear beam load cells

The outputs from the different load cells are summed to give the total vessel weight.

Three load cells are often best

For vertical cylindrical vessels, the chapter says three load cells spaced 120° apart is optimal.

Why?

Because three points define a stable plane. With three supports, the vessel naturally shares the load more evenly.

Four or more load cells can work, but they require more careful alignment. If one support is slightly higher or lower, the load may not be shared evenly.

Dummy load cells and pivots

The diagram on page 5 shows that sometimes some load cells can be replaced with dummies or pivots.

This reduces cost, but also reduces accuracy.

If only some supports are active load cells, scaling factors must be applied to estimate the total load correctly.

Handling and mechanical installation ⚠️

Load cells are robust in operation but can be damaged by sudden mechanical shock.

They are especially vulnerable when a vessel is being lowered into position.

The recommended method is:

1. Install the vessel without the load cells.
2. Jack the vessel up.
3. Carefully insert the load cells underneath.

This avoids accidental impact damage.

Vertical alignment

The load being measured and the load cells must be aligned vertically.

If the force is not vertical, the load cell may experience sideways forces, bending, or torque. These can distort the reading.

To reduce sideways loads, mountings often allow a small amount of sideways movement.

However, the mountings must also include safety constraints so the vessel cannot:

• fall off the cells
• shift due to vibration
• lift up under abnormal conditions

Shear beam bolts

For shear beam load cells, the mounting bolts must be:

• high tensile steel
• correctly torqued

If the bolts stretch, they can distort the readings.

This is a good example of how mechanical installation affects measurement quality.

Pipework problems 🚰

Pipework connected to a vessel is a major source of weighing error.

Why?

Because pipes can exert forces on the vessel. The load cells may then measure not only the vessel weight, but also mechanical stress from the pipework.

Good pipework design

The chapter recommends:

• pipelines should enter the vessel horizontally, not vertically
• pipelines should be distributed around the vessel, not clustered on one side
• longer pipelines with bends are better because they are more flexible
• short flexible pipe sections can eliminate many external pipework stresses

This is very important in industrial weighing. A vessel may have excellent load cells, but stiff pipework can ruin the measurement.

Moisture and cable glands 💧

Even though load cells are hermetically sealed, moisture can still seep in around the signal cable.

The cable gland must be sealed carefully.

This matters because moisture can affect the electrical signal and cause unreliable readings.

Key concepts to remember 🧠

1. Weight measurement often uses strain

Modern weight measurement usually works indirectly:

Weight → force → strain → resistance change → voltage signal

2. Strain gauges are sensitive but delicate

They measure deformation through resistance changes, but they require:

• correct alignment
• good bonding
• electrical insulation
• moisture protection

3. Temperature compensation is essential

Resistance changes with both strain and temperature. Wheatstone bridge arrangements with active and dummy gauges help cancel temperature effects.

4. Load cells make strain gauges practical

Load cells protect strain gauges and place them in a controlled mechanical structure.

5. Installation can make or break accuracy

Even a perfect load cell can give poor readings if:

• the vessel is misaligned
• pipework adds external forces
• bolts stretch
• moisture enters the cable gland
• the load cell is damaged during installation

Simple analogy 🎒

Imagine you are standing on a bathroom scale.

Inside the scale, your weight slightly bends a metal part. That bending is tiny, but strain gauges detect it through a change in electrical resistance.

Industrial load cells do the same thing, just with much more precision and durability.

So a load cell is basically a highly engineered version of:

“How much did this metal part deform when weight was placed on it?”

From that deformation, the system calculates the weight.

Final takeaway ⚖️

This chapter explains that modern industrial weight measurement is based on strain gauge load cells. A strain gauge changes resistance when stretched or compressed. Because strain is related to force through material mechanics, the resistance change can be calibrated into weight. But accurate measurement requires proper bridge circuits, temperature compensation, careful load cell design, and especially good installation. The electronics matter, but the mechanical setup matters just as much.