transmission line design structures & foundations...
TRANSCRIPT
Transmission & Distribution Program
Transmission Line Design Structures & Foundations
TADP 549
Steel Poles - Direct
Embedment Foundations -
Point of Fixity
Presentation 6.3
Dr. Prasad Yenumula
Reference Documents
RUS Bulletin 1724E-214, Guide Specification
for Standard Class Steel Transmission Poles
Poulos & Davis (1980), Pile Foundation
Analysis & Design
What is Point of Fixity?
Per RUS Bulletin 1724E-214,
“The point where the maximum moment
occurs. The actual location of this point is
dependent on the characteristics of soils
around the embedded portion of the pole”
Why it is important?
Location of Maximum Moment
For direct embedment poles, Maximum
moment occurs
– at the groundline or
– below the groundline
Depends on the soil/backfill conditions
At Maximum moment location, the shear
force is zero
Why is it Important?
Steel pole needs to be designed for
bending moments acting on steel pole
Steel pole section at point of fixity should
be sufficient to withstand the applied
bending moment
Theoretical Models
Let us consider Broms (1964) theory
– Cohesive soils (Clayey soils)
– Granular soils (Sandy soils)
Broms Theory (Cohesive Soils) Cont.
Source: Poulos & Davis, 1980
Broms Theory (Cohesive Soils) Cont.
Depth of point of fixity below the
groundline =
– 1.5d + f
– d=diameter of pole and f is as shown in figure
At depth of 1.5d + f below groundline, the
maximum bending moment occurs
Source: Poulos & Davis
Broms Theory (Cohesive Soils) Cont.
Equation for ‘f’
f = Hu / (9 cu d)
– Hu = Ultimate lateral capacity of soil
– d = Diameter of pole
– cu = Undrained shear strength of cohesive soil
Source: Poulos & Davis, 1980
Broms Theory (Cohesive Soils) Cont.
Equation for Maximum Moment (Mmax)
Mmax = Hu (e + 1.5d + 0.5f)
Note-maximum moment at groundline = Hue
– e = eccentricity of load
Source: Poulos & Davis, 1980
Illustrated Example - 1
A transmission pole structure of length 80
feet is to be installed in homogeneous
clayey deposit with undrained shear
strength of 3ksf using direct embedment
foundation
Determine the depth of embedment, point
of fixity and maximum bending moment
using Broms’ method. Water table is about
40 feet below the ground level
Illustrated Example - 1 (Cont.)
The thickness of the backfill annulus = 0.5
feet and the crushed rock backfill unit weight
is 140 pcf and friction angle 45 degrees.
The ultimate horizontal load at groundline
=40 kips and ultimate moment load at ground
line =2411 kip-ft
The average diameter of pole below
groundline is 3.7ft
Illustrated Example - 1 (cont.)
Solution
Because the hole is too narrow with relatively
stronger backfill, to make a conservative
estimate, it can be assumed that the failure
occurs in the surrounding in-situ cohesive
soil
The pole diameter should be considered in
the calculation. Now the problem is
simplified to rigid pile under lateral load
Illustrated Example - 1 (cont.)
Equation for ‘f’
f = Hu / (9 cu d) = 40/ (9x3x3.7) = 0.4 ft
Hu = Ultimate lateral capacity of soil=
equated to ultimate horizontal load
d = Diameter of pole
cu = Undrained shear strength of cohesive
soil
Illustrated Example - 1 (cont.)
Equations for Maximum Moment (Mmax)
Mmax = Hu (e + 1.5d + 0.5f)
Mmax = 2.25 cu d g2
Solved for g =10.283 ft by substituting
e = eccentricity of load = (M/H) = 2411/40 =
60.275ft
H = 40kips
f = 0.40 ft
Illustrated Example - 1 (cont.)
Total Foundation Depth = L = 1.5d + f + g
L = 1.5x3.7 + 0.4 + 10.283 =16.23 ft (minimum)
Depth of point of fixity below the groundline
=1.5d + f = 1.5*3.7 + 0.4 = 5.95ft
Maximum Moment (Mmax)
Mmax = Hu (e + 1.5d + 0.5f) = 40 (60.275 +
1.5*3.7 + 0.5*0.4) = 2641 kip-ft
Illustrated Example - 1 (cont.)
Ultimate moment load at ground line =2411
kip-ft
Maximum Moment (Mmax) = 2611 kip-ft
Pole section has to provide enough
resistance for the moment load at different
locations
Broms Theory (Granular Soils)
Source: Poulos & Davis, 1980
Broms’ Theory (Granular Soils) Cont.
Equation for ‘f’
f = 0.82 [Hu / (Kp d γ)]0.5
Hu = Ultimate lateral capacity of soil
γ = unit weight of the soil
Kp = Rankine’s earth pressure coefficient
Tan2(45+φ/2)]
d = diameter of pole
φ = angle of internal friction of the soil
Source: Poulos & Davis, 1980
Broms’ Theory (Granular Soils) Cont.
Equation for Maximum Moment (Mmax)
Mmax = Hu [e + (2f /3)]
– e = eccentricity of load
Source: Poulos & Davis, 1980
Broms’ Theory (Granular Soils) Cont.
•Hu = Ultimate lateral capacity of soil
•γ = unit weight of the soil
•L = embedded length of the pile
•Kp = Rankine’s earth pressure coefficient =Tan2(45+φ/2)
•φ = angle of internal friction of the soil
•e = eccentricity of horizontal load
•d = diameter of pole (‘B’ or ‘d’ are used for diameter)
L) + (e
d K L 0.5 = H
p
u
g 3
RUS Method
Simplified method
For RUS Standard class steel poles (RUS
Bulletin 1724E-214)
“For this specification it will be assumed
to be equal to 7 percent of the pole length
from pole butt”
RUS Method (Cont.)
* Foundation embedment depth = 10% of Pole Length + 2ft
**RUS Point of Fixity depth from Ground Line = Standard Foundation
Embedment depth - RUS Point of Fixity from Pole Butt
***Ratio of Depth = (RUS Point of Fixity depth from Ground Line) /
(Standard Foundation Embedment depth)
Let us Talk about Practice
Utilities may/may not provide point of fixity
information to pole manufacturer when they use
direct embedment poles
Manufacturer do not know site specific soil
information & foundation depth to determine this
point
Typically, Engineers who use pre-engineered steel
poles check pole section only at the groundline (and
above the groundline using design software such as
PLSPOLE)
Let us Talk about Practice (Cont.)
Because pole sections are tapered
– the extra section of pole below groundline
(compared to section of pole at groundline)
may likely compensate the extra moment load
at point of fixity - but needs to be checked!
Let us Talk about Practice (Cont.)
In fact, there may be an opportunity to
convert tapered section to straight section
from point of fixity
– Because moment loads decreasing after point
of fixity
– May be an economical consideration for deep
embedment pole sections
Cost of weld worth the transition from tapered to
straight section ?