Arch 4283 - Lecture 4: Spanning - Beams & Structural Systems

Flashcards covering structural spanning elements, beam stresses, bending moments, shear diagrams, deflection rules, section properties, and material behavior from Lecture 4 of Arch 4283.

What is the primary objective of Project 1 (The Table) in Arch 4283?

To study dead loads, bending, and column buckling while understanding materials, sizes, shapes, and structural force implications, emphasizing design rather than brute strength.

What are the primary material parameters and restrictions for Project 1 (The Table)?

The model must be built from exactly 1 sheet of $6\text{ inch}$ by $12\text{ inch}$ Strathmore 500 bristol board #3 (regular), with no glue, adhesives, paint sealing, metal sheets, or plastic members allowed.

What minimum load limit and duration are required to earn a grade of $90$ on Project 1?

The table must support 6 stacked, $12\text{ oz.}$ soft drink cans ($1.5\text{ pounds}$) at a minimum for at least $10\text{ seconds}$.

What is the exact load conversion value for a Kip?

$1\text{ Kip} = 1000\text{ Pounds}$.

How do code loads flow sequentially through a structural building system to the ground?

Loads are transferred horizontally across spanning members (such as beams and slabs) to vertical supporting members (such as columns and bearing walls), which transfer them directly to the ground.

What is internal shear force ($V$) in a structural beam?

The internal force resulting from an externally applied normal load, equal to the sum of all forces (loads and reactions) to the left of an imaginary section cut through the beam.

What is a bending moment ($M$) in a structural beam?

The rotational force equal to the sum of moments (force $\times$ distance) located to the left of an imaginary section cut through the beam.

What stress pattern is generated across a simply supported beam subjected to downward bending loads?

Compressive stresses are generated on the top concave face (shortening) and tensile stresses are generated on the bottom convex face (lengthening).

What does the steel designation $W12 \times 26$ specify?

A Wide Flange section ($W$) with a nominal depth of $12\text{ inches}$ and a weight of $26\text{ lbs.}$ per linear foot.

What is the neutral axis of a beam?

The internal plane across the cross-section at which the material experiences zero stress and strain, remaining at its original length between extreme shortening and lengthening regions.

What defines a cantilever beam?

A linear member with a fixed support at one end only, projecting outward into the air and loaded perpendicularly to its axis.

How do maximum shear ($V_{max}$) and maximum bending moment ($M_{max}$) compare between a simply supported beam and a cantilever beam carrying uniform load $W$ over span length $L$?

For a cantilever beam, maximum shear is doubled ($V_{max} = W$ vs. $V_{max} = \frac{W}{2}$) and maximum bending moment is four times greater ($M_{max} = \frac{WL}{2}$ vs. $M_{max} = \frac{WL}{8}$).

What is the point of inflection on a bending moment diagram?

The location where the bending moment diagram transitions from positive to negative values, corresponding to a moment value of $M = 0$.

How does beam deflection scale relative to changes in span length $L$?

Deflection increases as the cube of the span length ($L^3$).

Which cross-sectional and material properties inversely affect total beam deflection?

The moment of inertia ($I$) of the cross-section and the modulus of elasticity ($E$) of the material.

What formula calculates maximum deflection ($\text{Deflection}_{max}$) for a simply supported beam under a total uniform load $W_{total}$?

$\text{Deflection}_{max} = \frac{5W_{total}L^3}{384EI}$.

What is Section Modulus ($S$), and what is its equation for a rectangular section of width $b$ and depth $d$?

Section Modulus is a cross-sectional constant reflecting the proportionality between bending moment and maximum stress, defined for rectangular sections as $S = \frac{bd^2}{6}$.

What is the equation for the Moment of Inertia ($I$) of a rectangular cross-section?

$I_{rect} = \frac{bd^3}{12}$.

What formula relates allowable bending stress ($F_b$), bending moment ($M$), and section modulus ($S$)?

$F_b = \frac{M}{S}$.

In a stress-strain diagram, what property is defined by the slope of the linear elastic region?

Modulus of Elasticity ($E$).

How do low-carbon steel and high-carbon steel differ in ductility and strength?

Low-carbon steel is fairly strong and highly ductile, whereas high-carbon steel is much stronger but very brittle.

Why is steel reinforcement added to concrete in structural members?

Because concrete is strong in compression but weak and brittle in tension; adding steel provides substantial tensile strength and ductility to the composite member.

What mathematical relationship exists between the shear force diagram ($V$) and the bending moment diagram ($M$)?

The numerical value of the shear diagram at any point along the beam equals the slope of the bending moment diagram at that same point.