Formula for short term horizontal displacement

[Thila]

Hi All,
How to calculate the short term horizontal displacement (with adopting cracked section of the concrete) on free standing wall with eccentric footing at bottom, which is subjected to wind pressure alone. This is same as calculating torque of cantilever wall.

This is a plot boundary wall with eccentric footing. 

Thank you

[ANStructs]

Assuming the support of the wall is acting like an ideal fixed support, you can easily determine the deflection at the free end of a cantilever for uniformly distributed load using u=WL^3/8EI. To take into account the cracking of concrete you just need to use the effective moment of inertia in place of gross moment of inertia.

[Thila]

Thank you for your response. .

Can I take “Ig” instead “Ie”, if Mservice /Mcracking <1, .Because, Ms is not exceeded the cracking moment. Also , kindly review the calculation below. If it is not correct, kindly guide me. Thank you

This is cantilever wall rests in eccentric footing, subjected to wind. The calculation is considering wind load only. kindly find attached for sketch

 l                                      1.1 kN/m

 l_________________mmmmmmmmmmmm

 l        0.85m                        2.5m

 l----------------l----------------------l

 

B = 1000 mm (taken per meter width)

D = 120mm (thickness of wall)

 

Ig = 1000 x 120³ / 12 = 144x10⁶ mm⁴

 

n = Es/Ec = 200000/ 26587 = 7.52

Fr = 0.62 SQRT (32) = 3.56 N/mm2

Yt = 120/2 = 60 mm

 

Mcr = Fr*Ig/ yt = 3.56 *144x10⁶ / 60 = 8.544 kNm

 

Ma = 5.775 kNm

 

Ma/Mcr <1, Hence Ie = Ig

Deflection = w (uniformly distributed) *l⁴ / 8*E*Ig

 

w = 1.1 kN/m = 1.1 n/mm

loaded length = 2500 mm

total length = 3350 mm

E = 26587 n/ mm2

Ig = 144 x 10⁶ mm4

 

Deflection = 1.1 * 2500*2500* 2500*3350 / 8 * 26587 * 144x 10⁶

 

                    = 1.88 mm

[ANStructs]

On 12/15/2020 at 12:52 PM, Thila said:

Can I take “Ig” instead “Ie”, if Mservice /Mcracking <1, .Because, Ms is not exceeded the cracking moment.

Yes, your reasoning is right.

On 12/15/2020 at 12:52 PM, Thila said:

Also , kindly review the calculation below.

Calculation steps looks ok. But for calculating displacement, i would take L = 2.5 m since this is the length on which wind udl is acting.

If you want to take the full length of wall upto the base of footing, then you need to consider the soil lateral load on the wall as well.

[ANStructs]

Also, for full length of wall and different udl on wall, the formula for displacement will not be applicable.

[Thila]

Thank you. Can I consider pinned support at the earth top level as below??  I am modeling the same in SAFE too. 

[ANStructs]

I don’t believe that modeling the wall with a pin support at ground level resemble the actual condition of the wall. The model more close to reality will be a wall with lateral springs distributed along the embedded depth.

This is easier said than done, because, we all know that soil is not a linearly elastic material and calculating its lateral subgrade modulus will not be as easy as dividing the, let’s say, passive resistance with a correlating estimated deflection. And before you ask, No, I will not be of much help in calculating the said property of the soil because most structural engineers (including me) are in a state of blissful ignorance when it comes to the properties of soil. We mostly rely on our geotech counterparts to provide us with all pesky soil related properties, such as, allowable capacity and subgrade reactions.

Now as for solution to your problem if I were you, I’ll simply design the wall, for both serviceability and ultimate limit states, ignoring the soil on the passive side and considering the total length upto the base of footing loaded with wind and active soil pressure. This, I believe, will be a safer approach in case of a boundary wall, because, you can never be sure of the possibility if someone is not going to dig up the soil on the other side of the property in future.

[Thila]

Ok. Thank you.

But how can we ignore the soil fill load above the footing? How should we consider in calculating deflection.

If I consider only the wind and active pressure, deflection grows higher. Footing size and thickness of boundary wall also increases. 

To satisfy the overturning and sliding, 1.0m x 1.2m footing size is enough. But just because of this deflection criteria, footing size and also the thickness of wall increases. 

The below is link is related to the same discussion. FYI

https://www.sepakistan.com/topic/3126-short-term-cracked-deflection-for-cantilever-slab-in-safe/?tab=comments#comment-10203

[ANStructs]

On 12/24/2020 at 10:59 AM, Thila said:

But how can we ignore the soil fill load above the footing? How should we consider in calculating deflection.

Both the gravity and lateral load due to soil on the active side should be considered in the calculation. The soil resistance on the passive side however could be ignored to:

1.  Simplify the calculation.

2. There is a possibility that owner of the surrounding property can excavate the soil mass on the other side of the boundary wall in future without your consent.

3. Soil full passive resistance is something that develops as the soil mass is pushed due to significant wall rotation (approximately in order of 0.02 to 0.04 rad). And a designer would not really want this to be true for the serviceable live of the wall.

And, apologies for the delayed response.