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Note ARCH Set 14
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System Assemblies & Load Tracing
Load Tracing
LOAD TRACING is the term used to describe how the loads on and in the structure are transferred through the members (load paths) to the foundation, and ultimately supported by the ground. It is a sequence of actions, NOT reactions. Reactions in statically determinate members (using FBD's) can be solved for to determine the actions on the next member in the hierarchy. The tributary area is a loaded area that contributes to the load on the member supporting that area, ex. the area from the center between two beams to the center of the next two beams for the full span is the load on the center beam The tributary load on the member is found by concentrating (or consolidating) the load into the center.
ab
a
b
w=(
load ) x(tributary width) area
tributary width plan
where w = distributed load in units of load/length.
Distributed Loads Distributed loads may be replaced by concentrated loads acting through the balance/center of the distribution or load area: THIS IS AN EQUIVALENT FORCE SYSTEM.
w is the symbol used to describe the load per unit length. Note: It can also represent a load per unit area. W is the symbol used to describe the total load.
w x =W w x W = 2 2 w
w 0 x W
2w w x
x W/2
W W/2 x/2 x/6 x/3
x/2
x/2
2x/3
x/3
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ARCH 331
Note Set 14
F2008abn
Framing Systems Horizontal levels must transfer loads to vertical elements. There are many ways to configure the systems. The horizontal levels can be classified by how many elements transfer loads in the plane. Decking is not usually considered a level in a multiple level system because it isn't significantly load bearing. It is considered a level when it is the only horizontal element and must resist loads. Foundations The final path of the load for the structure is to the foundation. The foundation must transfer the loads to the soil, which is a "natural" structural material. The soil conditions will determine if a shallow foundation (most economical an easy to construct) can be used, or a deep foundation (for larger loads or poorer soil capacities) must be considered. Distribution of Loads on Edge Supported Slabs Distributed loads on two-way slabs (i.e. not one-way like beams) do not have obvious tributary "widths". The distribution is modeled using a 45 degree tributary "boundary" in addition to the tributary boundary that is half way between supporting elements, in this case, edge beams.
The tributary distribution from the area loads result in a trapezoidal distribution. Self weight will be a uniform distributed load, and will also have to be included for design of beam AB. Openings in Floor/Roof Plans Openings in a horizontal system usually are framed on all sides. This provides for stiffness and limiting the deflection. The edge beams may not be supporting the flooring, however, so care needs to be taken to determine if an opening edge beam must support tributary area, or just itself.
Any edge beam supporting a load has load on only one side to the next supporting element. 2
ARCH 331
Note Set 14
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Beams Supported by Other Beams Joists are commenly supported by beams with beam hangers. The reaction at the support is transferred to the beam as a single force. A beam, in turn, can be supported by a larger beam or girder, and the reaction from this beam having a uniform distributed self weight, and the forces, will be an action on the girder. Horizontal Projection of Gravity Load on a Rafter When an angled member, such as a rafter has a self weight per unit length, that weight is usually converted to a weight per horizontal length:
length wself wt . equiv . = wself wt . horizontal dis tan ce
Retaining Walls
Retaining walls are used to hold back soil or other material with the wall. The other key components include bases, counterforts, buttresses or keys. Gravity loads help provide resistance to movement, while the walls with lateral loads behave like cantilever beams. Loads The design of retaining walls must consider overturning, settlement, sliding and bearing pressure. The water in the retained soil can significantly affect the loading and the active pressure of the soil. The lateral force, P, acting at a height of h/3 is determined from the equivalent fluid weight (density), ', (in force/cubic area) as: 2 ph P= 2 where p is the maximum pressure at the base: p = h Overturning is considered the same as for eccentric footings: SF = M resist 1.5 - 2 M overturning 3
h/3
P
ARCH 331
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where Mresist = summation of moments about "o" to resist rotation, typically including the moment due to the weight of the stem and base and the moment due to the passive pressure. Moverturning = moment due to the active pressure about the toe "o". Sliding must also be avoided: SF = where Fhorizontal-resist = summation of forces to resist sliding, typically including the force from the passive pressure and friction (F=N where . is a constant for the materials in contact and N is the normal force to the ground acting down and is shown as R). Fsliding = sliding force as a result of active pressure. Pressure Distribution Because the resultant force from the gravity loads and pressure is not vertical, the vertical pressure distribution under the footing will not be uniform, but will be linearly distributed. The vertical component of the resultant must be in the same horizontal location as the pressure reaction force.
W P o R Fresist
Fhorizontal - resist 1.25 - 2 F sliding
There can never be a tensile pressure because the footing will not be in contact with the soil. To make certain all the area under the footing is used to distributed the load, the vertical resultant needs to be within the middle third of the base width. This area is called the kern. Soil pressure is most commonly called q in the design texts and codes.
3x Ry x
To determine the size of the maximim pressure we find the equivalent location of the pressure reaction, P, at x using moment calculations when Rx = W: W = P = 1/2p(3x) so and p = 2W/3x p = 2W/a when x < a/3 when x = a/3
p P = p(3x) a
where x is the location of the resultant force and a is the width of the base.
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ARCH 331
Note Set 14
F2008abn
Wind Load Tracing
For design purposes, wind loads are treated as static pressure distributions over the walls and roof. In the case of walls, the loads are traced just like those for horizontal surfaces. If there is a roof diaphragm, it is the "top" supporting element and the tributary boundary is half way "up" to the diaphragm. If the supporting elements are the side walls the tributary boundary is vertical and half way between sides. In either case, the traced action force at the top of the walls is a lateral shear force (V) that must be resisted. The shear over the width of a shear wall, v, is a unit shear used for determining the connection and framing capacity req...