External load E

A generic concentrated action applied at the wedge centroid. Use it to model road embankments, foundations of buildings, traffic loads, or vertical anchor reactions.

Parameters

Parameter	Symbol	Units	Notes
Magnitude	E	kN/m	per metre along the section direction
Inclination	δ	°	δ=0° horizontal toward the valley (unfavourable) · δ=90° vertical ↓ (weight) · δ=−90° upward (anchor reaction)
Load type	—	—	Permanent (γG) for structural weight, or Variable (γQ) for traffic/snow/accidental

Sign convention

• δ = 0°: horizontal, toward the valley (negative X direction). Typically unfavourable — destabilises the wedge.
• δ = 90°: vertical down (gravity-like). Acts as an extra weight applied at the centroid.
• δ = −90°: vertical up. Models a vertical anchor reaction (rare, but possible for cable-stayed structures).
• 0 < δ < 90°: tilted downward toward the valley (typical for embankments).
• 90 < δ < 180°: pushing toward the mountain — unusual, but supported.

Components

\[E_x = -E \cdot \cos\delta, \quad E_y = -E \cdot \sin\delta\]

The minus signs follow the "load pulling the wedge toward the valley" convention. Both E_x and E_y enter the global F_x, F_y together with the other actions.

Partial factor

• Permanent load → multiplied by γ_G (1.00 for NTC A2, 1.35 for EC7 DA1 C1 / DA2)
• Variable load → multiplied by γ_Q (1.30 for NTC A2, 1.50 for EC7 DA1 C1 / DA2)

On the section

E is drawn as an orange arrow from the wedge centroid G, oriented at angle δ from horizontal. If E is much smaller than W, the arrow is artificially elongated to remain visible (minimum 50 px); the label always shows the real magnitude.

When to use

• Road or rail embankment on top of the wedge: E ≈ 30–100 kN/m, δ ≈ 90° (vertical), permanent
• Building foundation: E from the structural design, δ ≈ 90°, permanent
• Traffic load: E ≈ 10–25 kN/m, δ ≈ 90°, variable
• Snow load: E from snow code, δ ≈ 90°, variable
• Inclined anchor reaction (rare): E from the anchor pull, δ between −90° and 0°, permanent