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The anchors contribute to the increase in strength resources for the bulkhead. The calculation of the limit load of an anchor must be made considering thee different collapse mechanisms. In fact, the collapse may happen by pull-out off of the bulb, by pull-out off of the steel part of the concrete which contains it or, possibly, by breaking of the anchor (reaching the threshold of the steel strength). The procedure used in the software calculates the limit load with regard to all three collapse mechanisms, and defines as limit load of the anchor the minimum between the three collapse mechanisms.

In this case, the limit load is calculated using the following formula (Schneebeli):

In the previous formula, the meaning of the symbols is the following:

σ'n is the effective stress acting in the center of the anchoring bulb

K is a coefficient which represents – on the average and for the whole length – the interaction between the bulb and the ground (see table)

Ab is the surface of the bulb in contact with the soil, evaluated using the following formula:

where D is the diameter of the bulb and Lb is the length of the bulb

ca is the adhesion to the interface between the bulb and the ground. Please look at the figure contained in the Anchors section for a better comprehension of the symbols.

ϕ

K

20°

1,3

30°

5,5

40°

30,00

Table: values provided in the work of Prof. Carlo Cestelli Guidi

"Geotecnica e tecnica delle fondazioni" ("Geotechnics and foundation engineering"), Vol. 2, Ed. Hoepli, year 1980.

In this case, the shear stress of ultimate adherence between steel and concrete is involved. The formula which expresses the collapse load of the system is the following:

In the formula, the symbols have the following meaning:

Da is the diameter of the reinforcement which constitutes the anchor

Lb is the length of the fastening bulb

τud is the adherence shear stress between steel and concrete

The design adherence shear stress fbd is:

fbd = fbk / γc

where:

γc is the partial safety coefficient related to concrete, equal to 1.5

fbk is characteristic shear resistance given by:

fbk = 2,25×η×fctk

where:

η = 1,0 for bars of diameter ϕ < 32 mm

η = (132 - ϕ)/100 for bars with bigger diameter

In case of very thickened reinforcements or anchorages in zone of stressed concrete, the adherence strength is reduced by diving it at least by 1.5.

Limit load for collapse by reinforcement failure

This is a purely structural check and concerns the circumstance in which the stress in the steel reaches the failure limit stress. In this case, the collapse load is calculated using the following formula:

In the previous formula, the symbols have the following meaning:

Da is the diameter of the reinforcement which constitutes the anchor

Fyd is the calculation yield stress of steel

Once the collapse loads have been calculated for the three different mechanisms, the limit load of the anchor can be determined using the following formula:

Where the symbols have the following meaning:

NuT is the ultimate limit load of the anchor

Nuat is the ultimate limit load which occurs for collapse in adherence between the bulb and the ground

Nuac is the ultimate limit load which occurs for collapse in adherence between the bulb and the steel

Nur is the ultimate limit load which occurs for collapse of the anchor's steel

For each anchorage, the failure mechanism is returned: ground failure, adherence resistance, steel resistance