Point, Distributed, Bearing & Pressure Loads

What Are Point, Distributed, Bearing and Pressure Loads?

Loads act on structures with different spatial distributions. A point load is a force concentrated at a single location. A distributed load is a force spread over a length, area or volume. A bearing load is a contact pressure distributed over a finite area — a bolt bearing on a hole, a pin in a lug, a roller on a rail. A pressure load is a force per unit area acting on a surface — aerodynamic pressure, hydrostatic pressure, internal pressure. The distinction between these load types is not academic — it determines how the load should be represented in a structural model and what local behaviour it produces. Applying a point load where a distributed load should be used, or vice versa, can introduce artificial stress concentrations or miss the real peak stress entirely. The engineer must choose the representation that matches the physical reality and the engineering question.

APPLY THE LOAD WITH THE SPATIAL DISTRIBUTION REQUIRED BY THE ENGINEERING QUESTION. A point load is an approximation; a distributed load is a representation; a pressure is a physical field. Use the one that the physics demands and the question requires.

Why Distribution Matters

The same total force can produce very different structural responses depending on its distribution. A concentrated load of 50 kN applied at a single node produces a theoretically infinite stress at that node — a singularity. The same 50 kN distributed over a 100 mm × 100 mm area produces a uniform pressure of 5 MPa with no singularity. The same 50 kN distributed as a bearing pressure over a bolt hole produces a peak pressure at the edge of the contact that is higher than the average but finite and physically meaningful. The distribution is not a detail — it is part of the load definition. An engineer who applies a concentrated load where the physics demands a distribution is introducing an artificial stress concentration that has no physical basis and that will drive the design in the wrong direction.

Point Loads and Their Limitations

A point load is a force applied at a single point. In reality, no load is truly at a point — even the sharpest contact has a finite area — but the point-load approximation is useful when the application area is small compared to the structural dimension. A point load is adequate for global bending analysis of a beam, where the exact distribution over a small region does not affect the overall bending moment. It is not adequate for local stress analysis at the load introduction point, where the distribution governs the peak stress. In finite element analysis, a point load applied at a single node creates a stress singularity — the stress at that node increases without bound as the mesh is refined. This is a mathematical artefact, not a physical result, and it must not be used for margin calculation. If the engineering question is about local stress at the load introduction, the load must be distributed over a finite area.

Distributed Loads: Line, Area and Volume

A line load is a force per unit length (N/m), applied along a beam or edge. A pressure is a force per unit area (N/m² or Pa), applied over a surface. A body force is a force per unit volume (N/m³), applied throughout a volume — gravity and inertia are the most common body forces. Each type has a different physical origin and a different representation in the structural model. Line loads are applied to beam elements or edge elements. Pressures are applied to shell or solid surface elements. Body forces are applied to all elements with mass. The choice of load type must match the physical reality: a wind load on a building facade is a pressure on the surface, not a line load on the frame; gravity is a body force, not a point load at the centre of gravity (although the resultant acts there for global equilibrium).

Pressure Integration and Resultants

The resultant force from a pressure distribution over a surface is the integral of the pressure over the area. The resultant acts at the centre of pressure — the point where the total force would produce the same moment as the distributed pressure. For global analysis — overall bending, overall shear, reactions — the resultant and centre of pressure may be sufficient. For local analysis — panel stress, skin buckling, local fatigue — the full pressure distribution must be retained. The engineer must know when the resultant is enough and when the distribution is required.

Pressure resultant and centre of pressure:

  Resultant force:
    F = ∫A p dA

  where:
    F = resultant force (N)
    p = pressure at each point (Pa)
    dA = differential area element (m²)
    A = surface area

  Centre of pressure:
    x_cp = (∫A x · p dA) / F
    y_cp = (∫A y · p dA) / F

  For uniform pressure:  centre of pressure = centroid of area
  For varying pressure:  centre of pressure shifts toward
                         the region of higher pressure

  Pressure as force over area:
    p = F / A

Bearing Loads and Contact Pressure

A bearing load is a contact pressure distributed over a finite area where one body presses against another. The classic examples are a bolt bearing on a hole, a pin in a lug, a roller on a rail. The bearing pressure is not uniform — it is highest at the centre of the contact and decreases toward the edges, or in the case of a cylindrical contact, it follows a cosine-like distribution with the peak at the centreline of the load direction. The peak bearing pressure is higher than the average (force divided by projected area), and the ratio depends on the geometry and the clearance. For a close-fitting pin in a hole, the peak bearing pressure is approximately 4/π times the average. For a loose-fitting pin, the contact area is smaller and the peak pressure is higher. Representing a bearing load as a uniform pressure over the projected area is an approximation; representing it as a point load at the centre is a worse approximation that introduces a singularity.

Bearing load distribution — pin in a hole:

   Force F applied to pin
        ↓
     ┌───┐
     │ ● │  ← pin
     └───┘
   ┌───────┐
   │ ╱   ╲ │  ← hole (larger than pin)
   │╱     ╲│
   │  p(θ) │  ← bearing pressure distribution
   │╲     ╱│
   │ ╲   ╱ │
   └───────┘

   Bearing pressure (cosine distribution):
     p(θ) = p_max · cos(θ)   for |θ| ≤ π/2
     p(θ) = 0                 for |θ| > π/2

   Peak:    p_max ≈ (4/π) · (F / (d · t))
   Average: p_avg = F / (d · t)

   where d = pin diameter, t = plate thickness

   Do NOT model as a point load — singularity.
   Do NOT model as uniform pressure — wrong peak.
   Model as cosine distribution or contact analysis.

Pressure Distribution Types

Pressure distributions take several common forms. A uniform pressure is constant over the area — the resultant is pressure times area, acting at the centroid. A linearly varying pressure changes linearly over the area — hydrostatic pressure increases with depth; the resultant acts at the centroid of the pressure prism (one-third from the base for a triangular distribution). A spatially varying pressure changes arbitrarily over the area — aerodynamic pressure fields, contact pressure distributions, wind pressure on complex shapes. The spatially varying case is the most general and the most common in real engineering — the pressure at each point is different, and the full field must be mapped to the structural model for accurate local analysis.

Singularity Avoidance in FEA

A singularity in finite element analysis is a point where the computed stress increases without bound as the mesh is refined. Point loads, point constraints, sharp re-entrant corners and material discontinuities at a single node all create singularities. A singularity is a mathematical artefact of the discretisation, not a physical result — real materials yield, real contacts distribute over a finite area, real corners have a finite radius. The engineer must recognise singularities and avoid using them for margin calculation. The remedy is to apply the load with its physical distribution: distribute a point load over a finite area, apply a bearing load with a cosine distribution, model a corner with a finite radius. If the engineering question is about the local stress at a load introduction, the load must be represented with its physical distribution — not as a mathematical point.

CONSIDERATION: A stress singularity in FEA is a warning, not a result. If the stress at a point increases as the mesh refines, the load or constraint is being applied in a physically unrealistic way. Distribute the load, model the contact, or radius the corner — and the singularity will resolve into a finite, physically meaningful stress.

When the Resultant Is Sufficient

Not every analysis requires the full pressure distribution. For global bending of a beam under a distributed load, the resultant force at the centre of pressure gives the correct bending moment and shear. For overall reactions and equilibrium, the resultant is sufficient. For global load balancing between subsystems, the resultant and centre of pressure are enough. The engineer must distinguish between questions that require the distribution (local stress, panel buckling, fatigue at a hotspot) and questions that are answered by the resultant (global bending, reactions, interface loads). Using the full distribution when the resultant would suffice wastes effort; using the resultant when the distribution is needed produces wrong local stresses. The engineering question determines the level of detail required.

Common Mistakes in Load Distribution

COMMON MISTAKE: Applying a point load at a single node for local stress analysis. The point load creates a singularity — the stress is unbounded and the margin is meaningless. If the engineering question is about local stress at the load introduction, the load must be distributed over a finite area that represents the physical contact.

Verification: Load Distribution Check

LOAD CHECK: For every load in the model, verify that the spatial distribution matches the physical reality. If the load is a contact, use a bearing distribution. If the load is a fluid pressure, use a pressure field. If the load is a body force, apply it through the mass. Check that no load introduces a singularity at a location where margin will be assessed.

Key Takeaways

• The spatial distribution of a load is part of its definition — the same total force with different distributions produces different structural responses
• A point load is an approximation that creates a singularity in FEA — use it only for global analysis, never for local stress at the load introduction
• A bearing load has a non-uniform distribution (approximately cosine for a cylindrical contact) — the peak is higher than the average
• Pressure resultants and centres of pressure are sufficient for global analysis but insufficient for local stress — the distribution must be retained for local work
• Apply the load with the spatial distribution required by the engineering question — not the distribution that is easiest to apply in the software