Module 2 – Forces and Moments in Piping Systems

Understanding Forces and Moments in Piping Systems

Piping systems are everywhere—power plants, oil refineries, chemical factories, and even water supply networks. But have you ever thought about what keeps them intact despite pressure changes, temperature swings, and external forces? That’s where forces and moments come in.

If a pipe could talk, it would tell you about the constant push, pull, and twists it experiences—from the fluid inside, the weight it carries, and even the occasional shake from earthquakes, wind, or machinery vibrations. Let’s break down these forces and moments and understand their real-world impact on piping systems.

Forces in a Piping System

Forces in a piping system come from two major sources:
1️⃣ Internal forces – caused by the fluid moving inside the pipe.
2️⃣ External forces – caused by environmental or structural factors.

1️⃣ Internal Forces: Pressure & Flow Effects

Inside a pipe, the fluid (water, gas, steam, or chemicals) is always in motion, generating two major internal forces.

🔹 a. Pressure Forces

Think of a garden hose—when you turn on the tap, water pushes against the inner walls of the hose. That push is a pressure force.

Now, imagine a large industrial pipeline carrying steam at high pressure—the internal force is massive. If not managed properly, the pipe could bulge, crack, or even burst.

🔹 Formula for Pressure Force

 F=P×A

where:

• $F$ = Force due to pressure (N)
• $P$ = Internal pressure inside the pipe (Pa)
• $A$ = Cross-sectional area of the pipe (m²)

📌 Example:
A pipeline carrying compressed air at 5 MPa with a diameter of 0.5 m experiences an outward force of:

$$F = (5,000,000) \times \left( \frac{\pi}{4} \times (0.5)^2 \right)$$

The larger the pipe and the higher the pressure, the greater the force pushing outward!

🔹 b. Flow-Induced Forces

Now, imagine water rushing through a bend in the pipe. Just like a car taking a turn, the fluid changes direction, creating a force against the pipe walls.

If the flow suddenly stops (like when a valve closes too quickly), it causes a water hammer—a loud bang due to a sudden pressure surge, which can crack pipes or damage valves.

📌 Example:
Ever heard a clanking noise in household plumbing when turning off a tap suddenly? That’s a mini water hammer!

2️⃣ External Forces: The World Outside the Pipe

Pipes don’t just deal with what’s inside them; they also face external forces.

🔹 a. Gravity (Dead Load)

Pipes and the fluids inside them weigh a lot. If not properly supported, pipes can sag, crack, or even snap.

📌 Example:
A long steam pipeline without proper support will start bending under its own weight, causing stress buildup and eventual failure.

🔹 b. Thermal Expansion Forces

Ever noticed how metal expands on a hot day? The same thing happens in pipes carrying hot steam or chemicals. When they cool down, they contract.

If this movement isn’t accounted for, pipes can crack, joints can fail, or severe stress can build up.

🔹 Formula for Thermal Expansion Force

 F=E×A×α×ΔT

where:

• $E$ = Young’s modulus (Pa)
• $A$ = Cross-sectional area (m²)
• $\alpha$ = Coefficient of thermal expansion (1/°C)
• $\mathrm{\Delta }T$ = Change in temperature (°C)

📌 Example:
A steam pipe in a power plant may expand several centimeters during operation. Expansion joints and flexible loops are used to absorb this movement and prevent failure.

🔹 c. Seismic and Wind Forces

In areas prone to earthquakes or strong winds (especially offshore platforms), pipes experience lateral forces that can cause them to sway, crack, or detach.

📌 Example:
During an earthquake, a refinery’s pipeline network needs flexible supports and dampers to prevent damage.

Moments in a Piping System

Forces are straightforward, but moments (torques) involve rotation and twisting of pipes.

1️⃣ Bending Moments: How Pipes Bend Under Load

🔹 What is a Bending Moment?

Imagine a long pipe supported at both ends, with a heavy valve in the middle. The valve’s weight pulls the pipe downward, causing it to bend.

🔹 Formula for Bending Moment

M=F×d

where:

• $\mathrm{M }$= Bending moment (N·m)
• $\mathrm{F }$= Applied force (N)
• $\mathrm{d }$= Distance from the force to the support (m)

📌 Example:
A pipe bridge carrying liquid across a gap needs extra supports to handle bending moments. Without proper support, the pipe may crack or collapse.

2️⃣ Torsional Moments: The Twisting Effect on Pipes

🔹 What is a Torsional Moment?

Think about wringing out a wet towel—you’re applying a twisting force. In pipes, this happens when:

🔹 Formula for Torsional Moment

$$T=F\times r$$

where:

• $T$ = Torsional moment (N·m)
• $\mathrm{F }$= Force applied perpendicular to the pipe (N)
• $r$ = Radius of the pipe (m)

• Rotating Equipment (Pumps, Turbines, and Compressors)

One of the most common causes of twisting in pipes is rotating equipment like pumps, turbines, and compressors.

🔹 How Does It Happen?

✔ When a pump spins fluid at high speed, it imparts rotational energy to the liquid.
✔ As the fluid enters the pipe, it carries some of that twisting motion, creating a torque inside the pipe walls.
✔ If the pipe isn’t properly supported or anchored, it may start to twist or vibrate, especially at bends and joints.

📌 Example:
In large oil refineries, high-speed centrifugal pumps move fluids at tremendous speeds. If the discharge pipe isn’t secured properly, it can start rotating slightly over time due to continuous torque from the pump. This can cause flange loosening or weld cracking at pipe connections.

•  Uneven Fluid Flow (Asymmetrical Flow Patterns)

Not all fluids move through a pipe in a straight, uniform manner. Sometimes, fluid velocity is higher on one side of the pipe than the other, causing a twisting effect.

🔹 How Does It Happen?

✔ Irregular pipe routing with multiple bends and offsets can create torque due to unequal force distribution.
✔ The faster-moving fluid on one side pushes harder than the slower-moving side, creating a twisting force along the pipe.

📌 Example:
In a chemical processing plant, a partially blocked strainer in a pipe caused uneven flow distribution. The fluid’s momentum shift generated torque, which led to gradual misalignment of the connected equipment.

• Thermal Expansion & Uneven Heating

Heat doesn’t just make pipes expand linearly—it can also make them twist if the expansion is uneven.

🔹 How Does It Happen?

✔ In systems with steam or high-temperature fluids, one side of a pipe may heat up faster than the other.
✔ As metal expands unevenly, it creates an internal stress difference, leading to a gradual twisting motion.

📌 Example:
A long overhead steam pipe in a power plant experienced uneven heating from direct sunlight. Over time, this caused the pipe to twist slightly, which put extra stress on its expansion joints, leading to premature failure.

• Seismic and Wind Forces on Exposed Pipes

For pipes located outdoors—on rooftops, offshore platforms, or above-ground pipelines—environmental forces like wind and earthquakes can apply unexpected torque.

🔹 How Does It Happen?

✔ High wind pressure can create a twisting force, especially on tall vertical pipes or pipelines running along bridges and supports.
✔ Seismic activity causes rapid ground movement, which twists and shakes pipes in multiple directions.
✔ Uneven support settlement after an earthquake can create rotational stress in piping systems.

📌 Example:
During an earthquake, a gas pipeline running along a bridge experienced rotational forces due to uneven movement of the bridge supports. This twisting led to stress fractures at welded joints, causing dangerous gas leaks.

• Unbalanced Pipe Supports or Poor Clamping

Even if no external forces are acting on a pipe, improper support placement can cause twisting over time.

🔹 How Does It Happen?

✔ If one side of a pipe is more tightly clamped than the other, it can create an uneven force distribution.
✔ Over time, small movements in the pipeline (due to vibration or thermal expansion) turn into twisting stress at weak points.

📌 Example:
A high-pressure water line in a food processing plant was secured with supports at irregular intervals. Over several months, slight movement from pump vibrations caused the pipe to develop a gradual twist, loosening flanges at one end.

3️⃣ Axial Forces: The Stretching and Compression of Pipes

🔹 What are Axial Forces?

Axial forces act along the length of the pipe, either pulling it apart (tension) or pushing it together (compression).

🔹 Formula for Axial Force

$$F_a=A\times \sigma$$

where:

• $F_a$ = Axial force (N)
• $\mathrm{A }$= Cross-sectional area (m²)
• $\sigma$ = Axial stress (Pa)

📌 Example:
A long underground pipeline may experience compressive axial forces due to soil movement, leading to buckling if not properly designed.

How Do These Forces and Moments Affect Piping Systems?

If left unchecked, these forces and moments can cause:
⚠ Pipe Stress and Fatigue – Continuous pressure and movement weaken pipes.
⚠ Leaks and Failures – Excessive stress at joints and bends can lead to cracks.
⚠ Unwanted Vibrations – Machinery-induced forces can damage pipes.

How Engineers Solve These Issues:

✔ Pipe Supports & Hangers – Prevent sagging.
✔ Expansion Joints – Absorb thermal movement.
✔ Stress Analysis Software – Predict weak points before installation.

P = Internal Pressure

$A$ = Pipe Cross-Sectional Area

$D$ = Pipe Outer Diameter

$t$ = Pipe Wall Thickness

$L$ = Pipe Length

$\mathrm{T }$= Torque

$r$ = Pipe Radius

$E$ = Modulus of Elasticity

$\alpha$ = Thermal Expansion Coefficient

$\mathrm{\Delta }T$ = Temperature Change

$\rho$ = Fluid Density

$c$ = Speed of Sound in Fluid

$\mathrm{\Delta }V$ = Change in Fluid Velocity

Final Thoughts

Piping systems may look simple, but they handle complex forces every second. By understanding and managing these forces, engineers ensure that pipelines in industries, cities, and homes remain safe and reliable for years to come. 🚀