Spring Stiffness of Tendon System & elastic Modulus of Tendon 2

[InDepth]

See attached.
1) Does anyone have any current data or sources that provides an average E of prestressing tendons based on diameter, # of strands, and material grade/relaxation property? Similar to table 2-2. From what I see, strand tendons are not as stiff as bars tendons (if equivalent length and area).

2) How do geotechs convert the assembly of tendon (strand vs bar vs size) and grout/ground stiffness into an equivalent spring for analysis?

Is there a good paper or resource that can explain the conversion from design to model? If springs weren't used, how would 2-D FEM account for the tendon stiffness.

 

[PEinc]

A threadbar/strand supplier can give you the values for E of each tendon type. Call DSI or Williams Form Engineering Corporation.

 

[Erdbau]

On a 7-wire strand, I've used 27000 ksi. This accounts for the unwinding of the tendon during stressing (as I believe your reference mentions).

For an equivalent spring, you can base it on the elastic elongation of the length of the unbonded zone plus half of the unbonded zone.

 

[PEinc]

I was given the following Modulus of Elasticity (E) values by DSI (Dywidag Systems):
7-wire strands - 28,500 KSI
GR150 Threadbars - 29,700 KSI

 

[InDepth]

Thanks Erdbau and PEinc. It looks like PTI and ASTM indicate the values provided by PEinc. Interestingly enough there is commentary indicating +/- 2.5% difference that should be accounted for when enveloping an upper bound and lower bound stiffness based on manufacturer and unwinding.

Erdbau - in your commentary you meant "unbonded zone plus half bonded zone" correct? I would assume this would apply for grouted and post grouted tendons....based on the assumption that half the grout in the bonded zone is in tension and half in compression? Would this be different for any other types of anchors such as compression anchors?

Thanks in advance

 

[PEinc]

If this is a ground anchor, you may easily exceed the maximum elastic stretch associated with the unbonded length plus half of the bonded length. According to PTI, if an anchor exceeds this elastic movemnent, it does not necessarily fail the proof or performance test. You are supposed to then investigate why you have too much stretch and find a satisfactory reason (Ref: PTI Recommendations for Prestressed Rock and Soil Anchors, Section 8.6.2.3). For a ground anchor with a bonded length through soil layers of various strengths (as is often seen with waterfront bulkheads), the anchor can often exceed the maximum elastic stretch as the anchor load transfers to deeper, stronger soil. For anchored jobs that I design, I always omit that acceptance requirement.

 

[Erdbau]

Yes, InDepth, my mistake: unbonded plus half the bonded. PEinc, you're absolutely right, but during design unbonded plus half bonded is a reasonable guess at the elastic length (unless you have reason to believe otherwise, of course). If you were predicting more stretch, are there any guidelines or studies about this? Seems hard to predict reliably.

 

[PEinc]

I'm unaware of any studies or guideline relating to actual unbonded length. You just need to look at the soil layers for the bond length and decide whether you think the anchor can be bonded in the upper layers without creeping and transfering the load deeper to more competent soils.

If you are trying to use FEA for a tiedback wall design, you may be using too powerful a tool for the accuracy of the input soil values. I believe the vast majority of tiedback wall designs use less sophisticated analysis tools.