Hammock post footing in clay

Geometry and loading

• Combined mass of two adults
• Standard gravity
• Baseline rope angle above horizontal, loaded
• Attachment height above finished ground
• Topsoil thickness over the clay
• Footing plan width (square)
• Footing depth, top flush with ground

Hammock loads at each support

With symmetrical suspension each support carries half the weight vertically. The rope's inclination above horizontal then sets the horizontal pull, V/tan θ, and the rope tension, V/sin θ. The pull acts through the post centreline at the attachment height, so the moment at finished ground level is the pull times that height.

These are static, unfactored actions from the occupants' weight alone. Climbing in, bouncing and swinging add inertia (the tension rises while the occupants accelerate, and swinging shifts load between the two supports), so the peaks exceed the static values. No dynamic amplification or partial factor is adopted here. Those belong to the standard the installation is assessed against, and inventing one would lend the comparison a precision it does not have.

• Weight of the occupants
• Vertical reaction at each support
• Horizontal pull at a support for a rope angle
• Rope tension for a rope angle
• Moment at finished ground level for a rope angle
• Baseline horizontal pull, static and unfactored
• Baseline rope tension
• Baseline moment at finished ground level
• Vertical equilibrium at the support
• The tension's horizontal component is the pull

Comparison across rope angles

A tighter hammock means a flatter rope. The vertical reaction is fixed by the weight, so the flatter the rope, the harder it pulls: the pull is V/tan θ and the tension V/sin θ, both growing without bound as the angle falls. At 10° each post is pulled sideways with 5.7 times the vertical reaction, against 1.7 times at 30° and exactly the vertical reaction at 45°.

The table reads back exactly by key. Between rows, linear interpolation follows the chord of a convex curve and overstates the pull by about 4 %: use the function for an untabulated angle, and keep interp() for genuinely tabulated data such as a code table.

• Horizontal pull, rope tension and ground-level moment at each support for five rope angles
• Baseline pull read back from the table by its angle
• The table agrees with the direct calculation
• Pull at 25° by linear interpolation between the 20° and 30° rows
• Exact pull at 25°
• Interpolation error of the chord

Soil assumptions

A hammock loads the footing for seconds to minutes, far less than the time this clay needs to drain, so the clay responds at constant volume and its resistance is governed by the undrained shear strength (the φ = 0 idealisation of Skempton, 1948). That makes a total-stress undrained assessment the appropriate short-term check. It says nothing about the long term: seasonal moisture change, surface softening and fissuring can lower the strength available to a lightly loaded shallow block, and a sustained pull would need a drained assessment.

• Assumed undrained shear strength, baseline

The simplified rotational model, assessed

The supplied model takes the footing as a rigid block rotating in the clay about a reaction-reversal depth below the clay surface: above it the front face mobilises a uniform limiting pressure of twice the undrained strength resisting the pull, below it the back face mobilises the same pressure the other way. Base adhesion, side-face shear and the resisting moment from eccentric bearing are omitted, the block does not pivot about its toe, and full passive pressure is not assumed on one face over the whole embedment.

That mechanism is the free-headed short rigid pile of Broms (1964), and the same force-and-moment balance underlies the embedded-post depth formula of IBC §1807.3. The uniform pressure of twice the strength equals the ground-surface term of the stiff-clay criterion of Reese, Cox and Koop (1975) and sits below Matlock's (1970) three times; both climb to nine to eleven times the strength with depth. Broms, by contrast, gives the top 1.5 widths in clay no resistance at all, which for this 0.4 m embedment would leave none.

So the model is a defensible idealisation for a comparison (low against published pressures at depth, optimistic against Broms at the surface), but omitting resistance components does not make it conservative overall, and it is not a validated design method. A better-supported assessment would treat the block as a short rigid pile with a depth-varying limiting pressure (Brinch Hansen, 1961), including base bearing and side shear, or apply the IBC embedded-post method; both need a measured strength profile, the clay unit weight and an allowable lateral bearing value, none of which is invented here. Every number from the supplied model is an illustrative model result.

The occupants' downward reaction and the footing's own weight press on the clay beneath the base; the resisting moment from that eccentric bearing is excluded from this lateral-only model. For a later alternative method, the vertical load it would bring:

• Unit weight of mass concrete
• Footing self-weight
• Vertical load on the base, excluded from the lateral model

Model geometry and resistance

Horizontal balance of the pull F against the front reaction q·a and the back reaction q·(D − a) gives F = q(2a − D). Moments about the clay surface, with the pull at height h above it, the front reaction at depth a/2 and the back reaction at (a + D)/2, give F·h = q(D²/2 − a²). Eliminating a: F(h + D/2) + F²/(4q) = qD²/4, a quadratic in F with the roots solved below without iteration.

• Attachment height above the clay surface, the model's moment datum
• Clay embedment of the footing
• Limiting lateral resistance per unit depth
• Limiting horizontal load at the attachment: the positive root, an illustrative model result
• The other root is negative: a pull the opposite way, not this case
• Reaction-reversal depth below the clay surface
• The reversal depth lies below the clay surface
• …and within the embedment
• Front reaction above the reversal depth
• Its depth below the clay surface
• Back reaction below the reversal depth
• Its depth below the clay surface
• Horizontal equilibrium: front minus back reaction equals the pull
• Moment equilibrium about the clay surface
• The supplied moment equation holds at the solution
• Corresponding moment at finished ground level

Sensitivity to the assumed strength

Only the horizontal pull enters the lateral assessment: the 1.47 kN rope tension is not the footing demand, its 1.27 kN horizontal component is. Even the 50 kPa case resists only 0.80 kN at the attachment, so the static demand exceeds the unfactored model resistance by a factor of 1.6 to 3.2 across the assumed strengths.

• The limiting pull as a function of the assumed strength
• Illustrative model results for the three assumed strengths; the last column is static demand over unfactored model resistance
• Baseline resistance read from the table by its strength
• Table and closed form agree
• Static horizontal demand over unfactored model resistance (not a utilisation or a factor of safety)
• Static pull within the model's limiting load

Limitations and interpretation

• Shallow embedment: at one width deep the footing sits entirely in the zone where soil can heave towards the free surface, which Broms excludes from resistance altogether.
• Three-dimensional behaviour: a 0.4 m block mobilises soil around its sides as well as its faces; a uniform plane-strain pressure of twice the strength is an idealisation, low at depth and optimistic at the surface.
• Base bearing, base adhesion and side-face shear all resist rotation and are omitted; their inclusion needs the alternative method and the inputs it lists.
• Seasonal drying, desiccation cracking, fissuring and surface softening of the clay reduce the strength available to a shallow block in summer and winter alike.
• Excavation disturbance and the quality of concrete-to-clay contact decide whether the assumed pressure can develop; a smeared or gapped face mobilises less.
• Limiting resistance needs rotation to mobilise: the post will lean before the clay yields, and a leaning post may be unacceptable long before the model's limit.
• Repeated and dynamic hammock loading: every swing cycles the faces, opening a gap on the unloaded side that softens the response over time.
• Serviceability versus ultimate resistance: a usable hammock post needs small movement under everyday use, a stricter criterion than the limiting load here.