33.2. Buildings Structures

There are three primary types of building systems:

1. Wall Subsytem: in which very rigid walls made up of solid masonry, paneled or braced timber, or steel trusses constitute a rigid subsystem. This is only adequate for small rise buildings.
2. Vertical Shafts: made up of four solid or trussed walls forming a tubular space structure. The tubular structure may be interior (housing elevators, staircases) and/or exterior. Most efficient for very high rise buildings.
3. Rigid Frame: which consists of linear vertical components (columns) rigidly connected to stiff horizontal ones (beams and girders). This is not a very efficient structural form to resist lateral (wind/earthquake) loads.

Buildings can be constructed using different frameworks, each serving specific needs:

1. Wall Subsystem: This type features solid walls that provide strength and stability for smaller buildings. For instance, solid masonry walls can withstand vertical loads and also provide insulation.
2. Vertical Shafts: These are designed for taller buildings as they allow crucial installations like elevators and staircases without compromising structural integrity. The tubular design helps distribute loads effectively over height.
3. Rigid Frame: This structure is made up of columns and beams that are connected at right angles. While it offers good load-bearing capacities, it may not withstand forces from high winds or earthquakes effectively due to a lack of lateral support.

Think of a wall subsystem like a small brick house that can easily stand up to the local weather but isn't built to be very tall. Imagine vertical shafts as the elevator shafts in a skyscraper that stretch from the ground to the top with the structural strength to support all floors above. Finally, a rigid frame is akin to a large tent with poles supporting a heavy canopy—great for holding up a roof, but if the wind picks up, it may wobble.

Whereas exterior walls provide enclosure and interior ones separation, both of them can also have a structural role in transferring vertical and horizontal loads. Walls are constructed out of masonry, timber, concrete, or steel. If the wall is braced by floors, then it can provide an excellent resistance to horizontal load in the plane of the wall (but not orthogonal to it). When shear-walls subsystems are used, it is best if the center of orthogonal shear resistance is close to the centroid of lateral loads as applied. If this is not the case, then there will be torsional design problems.

Walls in buildings do more than just provide separation between spaces; they also help carry loads. Let's break this down:

• Structural Functions of Walls: Walls can resist both the weight that comes down (vertical loads) and side pressures such as wind (horizontal loads). Materials like masonry and concrete are really strong for this purpose.
• Bracing and Load Distribution: If floors are connected to walls, this interaction improves the wall's ability to handle sideways forces. For example, a floor connected to a wall can help that wall resist the pressure of wind pushing against it.
• Importance of Load Centering: It's crucial for shear walls (walls designed to handle shear forces) to be positioned properly within a structure. If they are not aligned well with the center of forces (like wind), problems can arise where parts of the building twist or bend unpredictably.

Imagine a child holding a long board between two friends who stand at opposite ends. If they both push down simultaneously, they need to distribute their weight evenly to keep the board steady. The wall's connection to floors is like a child helping to hold the board steady, while placing the alignment precisely in the center is key to preventing twists or tipping.

We consider a reinforced concrete wall 20 ft wide, 1 ft thick, and 120 ft high with a vertical load of 400 k acting on it at the base. As a result of wind, we assume a uniform horizontal force of 0.8 kip/ft of vertical height acting on the wall.

In this example, we have a large concrete wall that needs to resist both a vertical load and wind pressure:

• Dimensions and Loads: The wall is tall and wide, having to carry a heavy load (400 k) at its base. Additionally, because it's affected by wind, we have to consider an extra lateral load which is applied uniformly along its height.
• Calculating Shear and Bending Moments: By understanding the total load and wind pressures, engineers calculate the maximum shear force and bending moments which indicate how the wall would behave under stress. These calculations are crucial for ensuring the wall can withstand these forces without collapsing.

Think about holding an umbrella upside down on a windy day. The vertical load is like how heavy the rain is pressing down on the umbrella, while the wind adds pressure from the sides. Just as you need to ensure the umbrella is strong enough to handle that weight and wind, our engineers make sure that the concrete wall can withstand both stresses.

1. Maximum shear force and bending moment at the base V = wL = (0:8) k.ft(120) ft = 96 k
2. The resulting eccentricity is M (5;760) k.ft
3. The critical eccentricity is L (20) ft therefore, there will be tension at the base.
4. The compressive stress of 740 psi can easily be sustained by concrete, as to the tensile stress of 460 psi, it would have to be resisted by some steel reinforcement.

Analyzing the stresses on a wall helps determine whether it can hold the imposed loads without failing:

1. Calculating Load Forces: The formula used helps determine how much force the wall needs to bear at its base due to wind pressure. This is essential for understanding whether the wall will remain stable.
2. Eccentricity Calculation: Eccentricity refers to the distance from the wall’s center of gravity to where the load is applied. If this value exceeds a certain limit, additional tension is created at the wall base, leading to stress concentration.
3. Understanding Stress Limits: Each material can only handle so much stress – in this case, concrete can handle compressive forces well but has limits on tensile stress, which needs reinforcing steel to manage effectively.

Visualize how much weight a person can lift using one arm. If they lift a heavy bag off-center, their arm may struggle and get hurt—that’s like the eccentricity causing extra stress at the base of the wall, requiring reinforcements (like lifting with two arms) to manage a heavier load.

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