Design Examples for Strut-And-tie ModelsFull description
Design Examples for Strut-And-tie ModelsFull description
Examples of Strut and Tie design
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Examples of Strut and Tie design
Descripción completa
Strut and tie.Full description
Examples of Strut and Tie design
Full description
Examples of Strut and Tie designFull description
Full description
Guide to Strut and Tie ModellingFull description
Structural Design of Pile Caps Using Strut and Tie ModelFull description
Beam Modelling Concept
Full description
Eurocode 6 design examplesFull description
9.1
Example 1 – Design of Cap Beam
f c' = 4ksi f y = 60ksi
Design Steps
1. Visualize flow of stresses and Sketch an idealized strut-and-tie model 2. Check size of bearing – nodal zone stresses 3. Select area of ties 4. Check strength of struts 5. Provide adequate anchorage for the ties 6. Provide crack control reinforcement 7. Sketch required reinforcement
9.2
9.3
Step 1 - Draw Idealized Truss Model Pier Cap Elevation
9.4
Step 1 - Draw Idealized Truss Model
9.5
Step 1 – Solve for Member Forces
Steps 2 thru 5 – Check Strength 5. Anchorage
3. Tension Tie 2. Size of Bearing
4. Compression Strut
9.6
Step 2 – Check Size of Bearings
Node D – CCC node – limiting stress of 0.85φ f c' Node A – CCT node – limiting stress of 0.75φf c' Node B – CTT node – limiting stress of
Pu
' 0.65 f c
259 2 bearing area required = = = 142 in. 0.65φf c' 0.65 × 0.70 × 4
9.7
9.8
Step 3 – Choose Tension Tie Reinforcement
a) Top Reinforcement over Column, Tie AB
Pu 295 2 = = 5.46 in. Ast = φ f y 0.9 × 60 Use 6 No. 9 bars
A s = 6.0 in.
2
9.9
Step 3 – Choose Tension Tie Reinforcement
b) Bottom Reinforcement at Midspan
Pu 605 2 Ast = = = 11.20 in. φ f y 0.9 × 60 Use 12 No. 9 bars
As = 12.0 in.
2
9.10
Step 3 – Choose Tension Tie Reinforcement
c) Stirrups, Ties BG & CH Try 2-legged No. 5 Stirrups
Pu 149 n= = = 4.45 φA st f y 0.9 × 2 × 0.31 × 60
60 s≤ = 13.5 in. 4.45 Provide No. 5 double-legged stirrups at 12 in
Step 4 – Check Capacity of Struts
• Strut FB is most critical • fcu controlled by tensile strain in tie at smallest angle to strut
Pu 295 εs = = = 1.695 × 10 −3 A st E s 6.0 × 29,000
f c' 4 = ≤ 0.85f c' = = 2.47 ksi ≤ 0.85 × 4 = 3.40 ksi − 3 0.8 + 170ε1 0.8 + 170× 4.81 × 10
Pn = f cu A cs = 2.47 × 17.7 × 30 = 1312 kips Pr = φPn = 0.70 × 1312 = 918 kips ≥ 671 kips required
9.14
Step 5 – Check Anchorage of Tension Tie
• Embedment length for No. 9 bars = 36 + 9 – 2 in. cover = 43 in. • Development length for No. 9 bars including top bar effect = 48 in. • Provide hooked bars
43 in.
Step 5 – Check Anchorage of Tension Tie
• Check nodal zone stress 295 fc = = 1.024 ksi 2 × 4 × 36
• Limiting nodal zone stress (5.6.3.6) is: f c = 0.75φf c' = 0.75 × 0.70 × 4 = 2.1 ksi
9.15
Step 6 – Provide Crack Control Reinforcement
• • •
D-region (region near discontinuity) Between nodes A & B 0.003 of Gross Area
•
Section §5.6.3.6
A s = 0.003 × 12 × 36 = 1.30 in. 2 • •
Provide 4 No. 5 bars horizontal (1.24 in2) Provide 4 legs of No. 5 stirrups
9.16
Step 6 – Provide Crack Control Reinforcement
• • •
A v = 0.0316 f c' • •
B-region (flexural region) Between nodes B & D Minimum Av per §5.8.2.5
b vs 36 × 12 = 0.0316 × 4 × = 0.46 in. 2 fy 60
Provided 2-legged No. 5 stirrups at 12 in. OK
9.17
Step 7 – Sketch the Required Reinforcement D - region
B - region
4 legged No.5 6 – No.9 stirrups at 12"
2 legged No.5 stirrups at 12"
4 – No.5
2 – No.5
6 – No.9 top 4 legs of No.5 closed stirrups @ 12" 4 – No.5 typ.