SS - Free Body Diagram and Determinacy Problems

SS - And Now For Something Completely Different

As of last month, I started taking courses to become a structural engineer. This, I thought, would be a nice complement to being an architect already.

If I'm to admit the truth, after taking several ARE exams, I've sort of reluctantly fallen in love with the idea of being structurally trained. The structures exams are widely considered the most difficult on the ARE, therefore one should (I believe) overcompensate in this realm of design. Reading the diaries of many architects, such as Frank Lloyd Wright and Mies van der Rohe, who enjoined their pupils to take on the science of the profession, further illustrates the truth that great architecture lies in great construction.

So this is a gift to you - namely, the homework problems that I've taken in my structural analysis courses. Enjoy.

BDCS Notes - Soundness of Aggregates

Aggregate Properties: Soundness and Durability

Soundness: The ability of aggregate to withstand weathering. Also called durability.

Soundness is desired in severe climatic conditions. Water freezing in the voids of aggregates generates stresses that can fracture the stones.

ASTM C88 – Simulates weathering by soaking the aggregates in either a sodium sulfate or magnesium sulfate solution. Sulfates cause crystals to grow in the aggregates, simulating the effects of freezing.

A sample is subjected to cycles of sulfate-soaking for 16 hours. Drying follows the soaking process. After five cycles, the aggregates are washed and dried, weighed, and the average percentage loss the entire sample is computed. The result is compared with allowable limits to determine whether the aggregate is acceptable.

BDCS Notes - Evaluation of Aggregate Sources

Evaluation of Aggregate Sources

Civil engineers select aggregates for how they meet specific project requirements, rather than their geologic history. The physical and chemical properties of rocks determine acceptability of an aggregate. Cost and availability are also key to consider when selecting an aggregate. Often, the wisest decision is finding out how to use locally available material in the most cost-effective manner.

Potential aggregate sources are evaluated for:

1. The quality of their larger pieces

2. The nature and amount of fine material

3. The gradation of aggregate

Drilling Cores / Trial Blasts – Investigate the extent and quality of rock in the quarry.

Cores and trial blasts also evaluate:

1. Grading

2. Particle Shape

3. Soundness

4. Durability

5. Amount of Fine Material

Cores are examined petrographically for:

1. General Quality

2. Suitability for Various Uses

3. Amount of Deleterious Materials

Sand and gravel pits are evaluated by:

1. Collecting Samples

2. Performing a Sieve Analysis

In an aggregate:

A high amount of large gravel and cobble sizes = NEED FOR CRUSHING

A high amount of fine material = NEED FOR WASHING

How aggregate can be used in a structure:

1. Used as a Base Material

2. Asphalt Concrete

3. Portland Cement Concrete

BDCS Notes - Geological Classification of Aggregates

Geological Classification of Aggregates

All natural aggregates result from breakdown of large rock masses. There are 3 kinds:

1. Igneous (rocks from volcanic action)
2. Metamorphic (exposed heat and pressure)
3. Sedimentary (exposed to weathering)

Igneous Rocks

Extrusive Igneous – Rocks formed by cooling at the surface

Intrusive Igneous – Rocks formed by cooling underground (in plutons)

Extrusive Igneous – Finer grain size and potentially include air voids and other inclusions.

Intrusive Igneous – Coarser grain size and fewer flaws.

Coarse grains = larger than 2mm

Fine grains = less than 0.2mm

Classification – based on silica content, specific gravity, color, and the presence of free quartz.

Sedimentary Rocks

Coalesce from deposits of disintegrated existing rocks or inorganic remains of marine animals. Wind, water, glaciers, or direct chemical precipitation transport and deposit layers of material that become sedimentary rocks, resulting in a stratified structure.

Bonds – formed by natural cementing of particles.

Classification – based on predominant mineral present:

1. Calcareous (limestone, chalk, etc.)

2. Siliceous (chert, sandstone, etc.)

3. Argillaceous (shale, etc.)

Metamorphic Rocks

Form from igneous or sedimentary rocks drawn back into earth’s crust and exposed to heat and pressure. Have crystalline structure, with grain sizes ranging from fine to coarse.

All 3 rocks are used successfully in civil engineering applications. The best possible prediction of aggregate suitability for a given application is based on historical performance in a similar design.

BDCS Notes - Aggregate Uses

Aggregate Uses

Aggregates are primarily used as:

1. An underlying material for foundations and pavements

2. Ingredients in portland cement and asphalt concretes

Aggregate underlying materials, or base courses, can add stability to a structure, provide a drainage layer, and protect the structure from frost damage.

Stability – a function of the interparticle friction between aggregates and the amount of clay and silt “binder” material in the voids.

Increasing the clay and silt content will block the drainage paths between the aggregate particles, thereby inhibiting the ability of the material to act as a drainage layer.

% Aggregate in Portland Cement Concrete

1. 60% to 75% of the Volume

2. 79% to 85% of the Weight

How Aggregate Works in PCC:

Aggregate acts as a filler to reduce the amount of cement paste needed in the mix. In addition, aggregates have greater volume stability than cement paste. Therefore, maximizing the amount of aggregate improves the quality and economy of the mix.

% Aggregate in Asphalt Concrete

1. 80% of the Volume

2. 92% to 96% of the Weight

How Aggregate Works in AC:

Asphalt cement acts as a binder to hold the aggregates together, but does not have enough strength to lock the aggregate particles into position. The result is the strength and stability of asphalt concrete depends mostly on interparticle friction between the aggregates and (to a limited extent) on the binder.

BDCS Notes - Aggregates

Aggregates

Two main uses of aggregates in civil engineering:

1. Underlying material for foundations / pavements
2. Ingredients in portland cement and asphalt concretes

Aggregates – combination of distinct parts gathered into a mass or a whole. Generally composed of individual parts gathered into a mass or a whole.

In Civil Engineering, an Aggregate is...

…a mass of crushed stone, gravel, sand, etc., predominantly composed of individual particles (which can sometimes include clays and silts).

Largest particle size in an aggregate = 150mm (6 inches)

Smallest particle size in an aggregate = 5 to 10 microns

Sources

Natural sources – Gravel pits, river run deposits, rock quarries. Gravels typically come from pits and river deposits. Crushed stones are the result of processing rocks from quarries.

Manufactured sources – slag waste from steel mills and expanded shale and clays. Produces lightweight aggregates. Heavyweight aggregate use steel slags and bearings. Styrofoam beads can be used as an aggregate in lightweight concrete for insulation.