EE 495/695Mechanical Considerations

Yahia Baghzouz, Ph.D., P.E.Electrical & Computer Engineering Dept.

Properties of Materials

Stress (force density) = force/area = P/AStrain (deformation) = elongation/length = ε= δ/lModulus of stiffness E = S/ εδ = PL/AE

Allowable Stress (should be well below the yield stress)

Sa= Sy/N, where N is a safety factor (which should be at least 2 to avoid accidental overloading).

Type of forces

Normal force (acting uniformly across a sectional area) – modulus of elasticity (E)Sheer force (acting tangentially to the area resisting the forces) – modulus of rigidity (G)

Column BucklingSome structural members of a PV array are long and slender – these can fail due to buckling under small compressive forces (compared to those that would cause failure due to crushing).The critical compressive force P that will cause the column to buckle is given by Euler’s Formula:

where L is the length, E is the modulus of elasticity, and I is the moment of inertia of its minimum cross sectional area.

2

2

LEIP π

=

Thermal Expansion /Contraction

Material contract and expand with temperature.The linear deformation of a structural member of length L is given by

where α is the coefficient of linear expansion and ΔT is the change in temperature.

TLt Δ=αδ

Chemical corrosionFailure of metal components by corrosion is as common as failuredue to mechanical stress.

Galvanic corrosion occurs uniformly due to the potential difference that exists between two dissimilar metals in contact with a corrosive of conducting solution. Use similar metals to minimize this.Crevice corrosion occurs at design details (e.g., holes, lap joints, etc…)Inter-granular corrosion is a localized attack along the grain boundaries of metals.Erosion corrosion (when corrosive fluid flows on metal surface)Stress corrosion (in cracking caused by stress)Dry corrosion (metal interaction with air)

UV Degradation

UV radiation is part of the electromagnetic spectrum having wavelength between 100 and 400 nm.Long term exposure to UV results in loss of skin elasticity and can cause skin cancer.Ultraviolet radiation can cause degradation and deterioration of some materials used in PV systems (e.g., weather sealing material, wire insulation, coatings, etc …)

Design and installation requirements

Design requirementsFunctional requirements: system capable of carrying all mechanical forces with an adequate degree of safety and lifetime (20-30 years)Operational requirement: periodic inspection and maintenance, ease of reach of fuses and circuit breakers, security (vandalism). …Constraints: cost, time, restrictive building codes, Trade-offs: Items subject to compromise when the desired objectives cannot be met (e.g., use steel rather than aluminum to save on cost)

Installation requirements:ASCE Std: Minimum Design Load for Buildings and other Structures.National Electric Code (NEC)

Forces Acting on PV ArraysDead weight, live weight, seismic effects, forces due to snow and ice, seismic activity, aerodynamic wind loading.

Dead load (weight of PV modules and structural members) – falls within 2-5 psf.Live load (weight of installation, inspection and maintenance crew) – less than 3 psf.Snow load (decreases with the tilt angle) – less than 8 psf.Seismic load: ASCE has detailed procedures for calculating these forces in earthquake-prone regions.Wind loading presents the most concern – can be greater than 100 psf.

Wind Load – drag force

Force from the wind depends on the atmospheric conditions (air pressure, temperature, viscosity and density)Bernoulli’s equation: p + 0.5ρV2 = constant (where p is the static pressure, ρ is the mass density, and V is the wind velocity) - worst case wind speed: 150 mphIn reality, friction and turbulence come into play which result in drag force

Wind load – lift force

Airflow over symmetrical airfoil.The positive angle of attack to the airflow results in significant lift.

Flat plates at different angles of attack to airflow

At perpendicular angle, there is a high drag and no lift.At other tilt angles, there is a vertical lift in addition to a drag.

Wind loading on PV array and support structures

Air velocity and pressure distribution is often complex (depends on terrain, nearby structures, direction of air flow, ground clearance, location within the array, etc …) → Empirical formulas are developed for estimating the structural loading resulting from exposure to various wind conditions usingwind tunnels.

Array Mounting System Design

Roof-mount arrays: stand-off (parallel to tilted roof surface)Rack mounting (above and tilted with respect to flat roof)Integrated mounting (building-integrated PV)Direct mounting (no airspace between module and roof).

Ground-Mounted arrays:Rack mountingPole mountingTrack-mounting

Stand-Off and Roof-Mount Examples(See Section 5.8)

Roof with a 4:12 slope,Design for both low and high wind speed casesRoof height: 12’Exposure B (area with numerous obstructions the size of a single family home per ASCE-7)Look-up tables (from ASCE-7) are used to determine wind load.