# Structural behavior of lateral load resisting systems with structural membranes

When designing a structure, there are two major loads to consider; the gravity load and the lateral load. While gravity load generally acts downward, a lateral load is considered to act in the horizontal (or sideways) direction. Lateral load manifests through wind and earthquakes. It is of utmost importance that a suitable path exists through which its force is transferred to the ground.

This article aims to investigate how lateral loads are being resisted by a few selected structural membranes.

**The lateral force-resisting system.**

**Pile Foundations**

Pile foundation do resist lateral loads via 3 major means;

- Passive soil resistance on the face of the cap
- Shear on the base of the cap
- Passive soil resistance against pile shaft

It is noteworthy that the third means is the most reliable.

When examining the issue that comes up in the structural design of pile foundations, factors such as soil reaction, rotations, deflection, and moment, shear and soil reaction are important for such analysis. This examination is often done using the Beam-on-elastic Foundation approach. This theory works because of the ability of most piles to change. This makes it possible for us to say that they have an extremely large length, for the sake of analysis only. But, when analyzing the short rigid piles, the lower boundary condition should be factored in as well.

Now, steady modulus-depth and linearly increasing relationship have non-dimensional solutions. However, some solutions have steeped variation of the modulus, k. The very large amount of experimental value helps us to choose the right variation of k with depth. These values of k oftentimes come as a function of observable soil features. The size of k, if needed can be determined through an experiment by adding the related non-dimensional solution with plain lateral load tests.

There are some important factors that influence effective modulus such as group action which brings about a 25 percent reduction in the effective modulus of a separated pile, a cyclic load that is capable of increasing deflection, and thus further reduces the effective modulus. The presence of these effects can make the effective modulus to reduce to 10 percent of that for the first loading of an isolated pile. This makes the quality of not changing hard to reach the top of the pile. A fixity of 50 percent is good most times as it provides almost the same positive and negative moments. With this in place, the uniform flexural members are applied in an efficient manner from a structural angle. So when fixity increases, the deflection will drop through increased stiffness.

A technique exists through which analysis can be carried out for partially embedded piles by using the non-dimensional solutions readily available for fully embedded piles. This is manipulated by introducing depth to fixity usually based on soil characteristics and pile stiffness, thus eliminating the problem of taking arbitrary depths to fixity. By conservatively assuming values for k, designs that are economical can be obtained. However, in cases where using more accurate design data can cause significant savings, a simple field test program can be conducted to generate the required data.

Piles must resist lateral loads and moment in addition to their primary loaded members. To achieve this, the designer must determine the deflections and stresses in the prevailing soil-pile system and then find innovative ways of controlling them until they lie within a tolerable range.

**The technique for Analyzing soil-pile interaction**

In addition to the usual gravity load, W, the cap is often subjected to moment and shear loads. The capacity of the pile axially is instrumental in resisting the axial load. However, this will not be considered here. The moment and shear loads are resisted by;

- A passive soil resistance on the face of the cap
- Shear along the base of the cap
- Moment and shear resistance of the piles at the junction to the cap.

It is then easy to see that the resistance to the moment and shear of the piles are dependent on the stiffness and strength of the pile and soil respectively.

Temporary forces like passive soil resistance can also resist lateral loads. They are temporary because basic alteration or repair jobs may remove their lateral load resisting abilities from the soil; as a consequence, they are usually neglected when an analysis is being made. Another temporary resistance to lateral loads is observed in the shear along the base of the cap; in a similar fashion, a slight settlement of the soil beneath the cap is enough to destabilize its resisting property and as a result, it is also neglected.

The moment and shear resistances are much more permanent and are the only factors considered when analyzing designs.

**Slab-Column Connections**

Structural systems for offices and industrial buildings are usually made up of reinforced concrete (RC) sported on columns. In fact, by adding reinforced concrete walls, the lateral stiffness and strength of the structure are drastically increased. These RC walls carry the bulk of the horizontal loads in the event of an earthquake.

The lateral stiffness and strength of a structure are quite independent of the slab-column system. The slab-column connection is designed to follow the displacements (caused by the vibration of the earth)s of the structure while ensuring that the vertical load-carrying capacity from slab to column isn’t compromised. If compromised, brittle punching failure occurs in the slab. Since the deformation capacity of the entire building is defined by the deformation capacity of the slab-column connection, excess compromise can lead to collapse.

In this section, we wish to present an analytical approach that can be employed in predicting the moment resistance of a mechanism that adds up to the strength of the slab-column connection under earthquake-induced drifts. This approach is hinged on the Critical Shear Crack Theory (CSCT). In addition, we will also consider the effect of gravity-induced loads on the behavior of slab-column connections under loading caused by the vibration of the earth and also mechanisms that help resist increasing drifts.

This system of RC supported on column offers many benefits for offices and industrial buildings such as wide open spaces and they are relatively faster to construct. In earthquake-prone areas, it is important to include vertical spines (shear and/or core walls) to increase the horizontal stiffness to enable it to withstand a great number of horizontal loads imposed by seismic activities. The slab-column system is excluded from the systems that resist lateral force.

If compromised, brittle punching failure can occur in the slab. Since the deformation capacity of the building is dependent on the deformation capacity of the connection, a large compromise can eventually lead to collapse.

When moment and shear force interacts with a slab-column connection, three mechanisms help to resist the moment. They include;

- Shear force eccentric to the column axis
- Flexure
- Torsion

It can be extremely convoluted to calculate the contributions of the resistant moments if the slab-column connection is subjected to a non-linear eccentric moment (NB such non- linearity can even be caused by a crack). This is magnified by the fact that the resistant moments withstand differing failure modes.

The mechanism of resistance to lateral load in slab-column connect has been investigated by several researchers. The common experimental method for experimentally determining the contribution of flexure and torsion mechanism was developed by Hanson and Hanson in 1968. Their method involves cutting slots in the slab in the neighborhood of the column faces. Other researchers (Kanoh and Yoshizaki, 1979) connected a column monolithically to a slab specimen. Thereafter, a force couple was then applied in such a way that torsion alone is transferred from the column to the slab. It is important to note that these experimental methods are limited in the application.

The design equations in codes of practice (ACI 318, 2011; Euro code 2, 2004) are also used in estimating these resistant moments. They are based on an empirical analysis that takes into consideration the contribution of the eccentric shear and the bending moment while neglecting the contribution from torsion.

Another important assumption made to simplify the equation is that the linear (ACI 318, 2011) or uniform (Euro code 2, (2001) distribution of shear stress on the critical perimeter. As a consequence, if the shear stresses are distributed in a non-linear or non-uniform fashion, the equation breaks down by either under predicting or over predicting the moment capacity of slab-column.

Furthermore, there exists a more widely accepted method of finding the moment transferred to the connection. However, the model fails to define the relationship between moment and deformation capacity.

It is essential to estimate the moment-rotation relationship and rotation capacity of the slab-column connection when designing and accessing buildings with flat slabs and columns to withstand drifts induced by seismic actions. The model used in the analysis and prediction of the moment-rotation relationship must incorporate the size effect, column size, gravity load effect, and reinforcement ratio influence.

**Wall Panel**

Under the action of wind and seismic loading, it is very important to understand the performance of walls panels in residential buildings. Dead and live gravitational loads effect wall panel. In addition, when exposed to these forces, wall panels are also influenced by in-plane shear and/or out-of-plane lateral forces.

There exist several studies that have been carried out to understand the behavior of wall panels under out-of-plane loading. Also, various design and prescriptive methods have been outlined for constructing wall panels in other to withstand this kind of duress. On the other hand, understanding the performance of in-plane forces requires further investigations. This investigation involved comparing the in-plane shear resistance of various types of wall panels commonly used in residential buildings.

Five plane specimens with an aspect ratio (height/length) of 2 were tested. Flexural From the experiment, using a standard test condition, it was discovered that ICF wall panels are much stronger and stiffer than similar wood- or steel-frame walls panels. In fact, ICF walls resisted between 6 to 8.5 times of the lateral loads resisted by framed wall panels.

Also, the initial stiffness of the ICF panel was between 18 to 38 times that of wood- or steel-frame wall panels. When ICF wall panels were subject to two times the maximum lateral load resisted by framed walls, the ICF wall was able to withstand it and even exhibit a linear behavior with no sign of physical damage of any sort. The deformation under this load level was in a range of 0.05 to 0.07 in.

However, the maximum deflection provided by the ICF wall panels equaled or exceeded by just 2% of the height of the building. This strength advantage of ICF wall panels gave it the ability to even withstand rind and earthquakes of much stronger magnitudes.

It is important to note that this study takes no account of the effect of dynamic and out-of-plane loading, opening in the panels and various wall configuration. Therefore, care should be taken not to extend the result to panel analysis during actual earth motion. Furthermore, Lateral deformation is limited in ICF wall panels because of their stiffness. Also, their stiffness prevents potential damage to the non-structural element of the building.

In the event of a moderate earthquake or wind, most of the damage suffered is prevalent on the non-structural components. Therefore, only these non-structural parts usually need repair. The connection between the wall panels and the footings and between the panels and the floor/roof can influence two major things which include;

- The behavior of the wall panels
- The development of an effective load transfer mechanism in the structure.

The lateral load distribution can also be influenced by the position of the wall panels in the building plan and roof/ floor diaphragm action.

From our results, we have been able to identify some design aspects that can be improved to enhance the in-plane shear behavior of the wall panel even at a reduced cost.

When using a wood frame, the use of screws (instead of nails which have a lower pull-out resistance) instead of nails for connecting the OSBs to the frame members would significantly increase the maximum lateral resistance. This is achieved through increased integrity that prevents premature separation of the boards from the frame.

For steel-frame wall panels, making use of stiffening plates, small screw spacing, eliminating web holes in the lower part of the vertical studs and making use of heavier gauge bottom tracks would ensure that premature buckling and bending of the frame member is avoided.

Finally, when using ICF wall panels, implementing a dowel with longer development lengths between the footing and the wall would ensure that early pull-out of the dowel is avoided. Also, it strengthens the base of the wall panel.

Its effectiveness can be further improved by accompanying the longer dowels with vertical reinforcing bars in the wall that possess.

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