Engineering
CIV4235
Advanced Structural Design
Strut and Tie Model (STM)
Practice class 3
Dr. Chua Yie Sue
Adapted from Dr. Ye Lu
Week 3 Learning outcomes
▪ Calculation of Bursting Force
▪ Design of Anchorage Zones
Dapped beam with hole (Example)
Step 1: Divide the beam into D- and B- regions;
Step 2: Calculate the load at supports: 160*(7+0.175*2)/2=588 kN
Dapped beam with hole
Step 3: Sketch a suitable STM
Dapped beam with hole
Step 4: Calculate the loads at nodes (proportional to UDL to be replaced)
Examples:
56 kN=160*0.175*2
152 kN=160*(0.65-0.175)*2
192 kN=160*(1.075-0.475)*2
Dapped beam with hole
Step 5: Calculate the loads of struts and ties
Section method of truss analysis:
F = 0
F = 0
M = 0
x
y
By using an imaginary line, the truss will be
cut into sections, each of which must be in
equilibrium if the entire truss is in equilibrium.
Example
F
y
= FXD sin  + 160 + 176 − 588 = 0
sin  =
750
7502 + 1100 2
FXD = 447 kN
M
about X
= FCD  750 + 160  1050 − 588  (1050 + 325)
=0
FCD = 854 kN
F
x
FCD
α
FXD
FXW
= FXD cos  + FCD − FXW = 0
cos  =
1100
7502 + 11002
FXW = 1224 kN
Dapped beam with hole
Step 6a: Determine the width/area of struts
Example: Node A
Assume node A is hydrostatic
Strut Check (strut AB):
𝐶 ∗ ≤ s𝑡𝐶𝑢 ≤ s𝑡𝛽s 0.9𝑓𝑐′ 𝐴𝑐
s =
1
2
1 + 0.66(cot )
 = 45o
 s = 0.6
0.3  s  1.0
Take fc’=40 MPa and width of web=350 mm
𝐶 ∗ ≤ s𝑡𝐶𝑢 ≤ s𝑡𝛽s 0.9𝑓𝑐′ 𝐴𝑐
𝐶 ∗ = 588/ sin 𝜃
588 × 1.414 × 103 ≤ 0.65 × 0.6 0.9 × 40 × 𝑤 × 350
𝑤 ≥ 169 mm
Node Check (A):
CCT nodes: βn=0.8
σ3 ≤ s𝑡β𝑛 0.9𝑓𝑐′
𝐶 ∗ ≤ s𝑡β𝑛 0.9𝑓𝑐′ 𝐴𝑐 (Valid for hydrostatic nodes only)
βn=0.8>βs =0.6
Strut requirement controls
Dapped beam with hole
Step 6b: Check sufficient room exists within the web and flanges to fit
the struts;
Step 7: Determine the steel reinforcement with consideration of
minimum area and detailing requirements;
Step 8: Decide the detailing.
Draw STM
Draw STM
P