b$)$ Gravity load path in a building frame: The goal of this exercise is to understand the gravity load path

in a steel framing system. We model a frame with a floor slab in LARSA and obtain maximum internal

forces in the joists, girders and columns. We also perform a hand calculation based on tributary areas

and application of equilibrium. We compare the two sets of results to gain an appreciation for how

the load path works, and also of one$-$way action of the slab.

Figure $1.$ Plan of framing system in Problem $($b$)$

The plan of the framing system is shown in Figure $1.$ In modeling this frame, the girders are connected to

the columns through shear connections $($modeled with moment releases at the girder ends$)$; similarly,

the joists are connected to the girders and columns also through shear connections. Two LARSA models

of this system are provided on UBlearns $-($i$)$ GravityLoadPath$-$ContinuousSlab. lar, in which

the concrete$-$on$-$metal$-$deck floor slab is modeled as rigidly connected to the beams $($i$.$e$.,$ both joists and

girderes$),$ so that the slab can be considered continuous, and $($ii$)$ GravityLoadPath$-$

SimpleSlab. lar, in which the slab is modeled as simply supported on the beams using DOF

constraints. In each model, a load case has been created with a uniformly distributed floor load.

Complete the following table.

Display moment diagrams from LARSA supporting the numbers above.

Answer the following questions.

I. What might be a motivation to model the slabs as simply supported in the model $($ii$)?$

II$.$ Explain the differences between the LARSA results and your hand calculations.

Specifically, based on your understanding of statically indeterminate structures, why do

you think joist $2$ in model $($i$)$ carries more load than in model $($ii$)$ and your hand

calculations?

III. Based on analysis results in models $($i$)$ and $($ii$),$ is approximating the slabs as acting one$-$

way justified in your hand$-$calculation? Why$/$why not? c$)$ Lateral load path in a building frame:

I. What members would you add to the framing in Figure $1$ to provide a reasonable load

path for lateral loads.

II$.$ Describe the resulting lateral load path.