Real engineers actually laugh at jokes about mathematicians .
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04/21/23 Secant Formula 1 of 62
Real engineers actually laugh at jokes about mathematicians.
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Ideal pin-ended compression members
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EI
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(with )
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Remember: 2 plus 2 is four, but adding a safety factor we will call it 5.
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Did they know that?
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4
4
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Oops: Collapse of the Second Narrows Bridge, Vancouver
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4
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04/21/23 Secant Formula 55 of 62
Pre-stressed Concrete
Stage 1Tendons and reinforcement are positioned in the beam mould.
Stage 2Tendons are stressed to about 70% of their ultimate strength.
Stage 3Concrete is cast into the beam mould and allowed to cure to the required initial strength.
Stage 4When the concrete has cured the stressing force is released and the tendons anchor themselves in the concrete.
04/21/23 Secant Formula 56 of 62
Prestressed Concrete
04/21/23 Secant Formula 57 of 62
Post-tensioned Beams Stage 1Cable ducts and reinforcement are positioned in the beam mould. The ducts are usually raised towards the neutral axis at the ends to reduce the eccentricity of the stressing force.
Stage 2Concrete is cast into the beam mould and allowed to cure to the required initial strength.
Stage 3Tendons are threaded through the cable ducts and tensioned to about 70% of their ultimate strength.
Stage 4Wedges are inserted into the end anchorages and the tensioning force on the tendons is released. Grout is then pumped into the ducts to protect the tendons.
04/21/23 Secant Formula 58 of 62
Post-tensioned Beams
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When the tensioning force is released and the tendons are anchored to the concrete a series of effects result in a loss of stress in the tendons. The effects are :
• relaxation of the steel tendons • elastic deformation of the concrete • shrinkage and creep of the concrete • slip or movement of the tendons at the anchorages during
anchoring • other causes in special circumstances, such as when
steam curing is used with pre-tensioning.
Total losses in prestress can amount to about 30% of the initial tensioning stress.
Loss of Prestress
04/21/23 Secant Formula 60 of 62
Arrgggh, it’s over!
04/21/23 Secant Formula 61 of 62
Burj Dubai Tower 800 metres (2,640
feet) tall Upward-spiral design
Exterior cladding system
Built of glass, aluminium, concrete,
steel Designed by
Skidmore, Owings & Merrill, Chicago
Total floor space of 500,000 sq m (5.35
million sq ft)
04/21/23 Secant Formula 62 of 62
Solution to Problem 3:
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