example i-1.pdf

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Example I-1: Composite Beam Design

A series of 45 ft span composite beams at 10 ft o/c are carrying the loads shown below. Thebeams are ASTM A992 and are unshored. The concrete has f'c = 4 ksi. Design a typical floorbeam with 3 in, 18 gage composite deck and 4.5 in normal weight concrete above the deck

for fire protection and mass. Select an appropriate beam and required number of shear studs.

≔Lbeam 45 ft

≔S 10 ft

≔tslab 7.5 in

Material Properties:

≔ F y 50 ksi ≔ F u 65 ksi ≔ E 29000 ksi [AISC Table 2-3, p. 2-39]

≔ f`c 4 ksi

Loads:

Dead load:

≔Slab 0.075kip

ft2

≔ Beam 0.008kip

ft2

(assumed)

≔ Misscellaneous 0.01 ―ipft

2(ceiling, hangers, etc.)

Live load:

≔Live 0.10 ―ip

ft2

(non-reduced)




Construction Load:

≔Constructiondead 0.083 ―ip

ft2

≔Constructionlive 0.02 ―ipft

2

Since each beam is spaced at 10 ft o/c:

=≔ Dead ⋅++Slab Beam Misscellaneous 10 ft 0.93 ―ip

ft

=≔Live ⋅Live 10 ft 1kip

ft

=≔Constructiondead ⋅Constructiondead 10 ft 0.83 kipft

=≔Constructionlive ⋅Constructionlive 10 ft 0.2 ―ip

ft

Calculate Factored Moment:

=≔wu +⋅1.2 Dead 1.6 Live 2.72 ―ip

ft

=≔ M u ――

⋅wu Lbeam2

8 687 ⋅ip ft [AISC Table 3-23, Example 1, p. 3-211]

Determine Effective Width:

The effective width of the concrete slab is the sum of the effective widths for each side of thebeam centerline which shall not exceed:

=≔beff min⎛

⎝

――2 Lbeam

8

―2 S

2

⎡

⎣

⎤

⎦

⎞

⎠

10 ft

[AISC§

I3.1, p. 16.1-83]

Calculate the moment arm for the concrete force measured from the top of the steel shape,

Y2.

Assume a = 1in (Some assumption must be made to start the design process. An assumptionof 1.0 in has proven to be a reasonable starting point in many design problems.)




≔atrial 1 in

=≔Y2 −tslab

atrial

2

7 in

Enter Manual Table 3-19 with required strength and Y2 = 7.0 in. Select a beam and nuetralaxis location that indicates sufficient available strength.

Select a W21x50 as a trial beam With PNA = BNL (See p 3-30, Figure 3.3c):

≔ϕb M n ⋅770 kip ft [AISC, Table 3-19, p. 3-177]

≔ flexural_strength if

else

≤ M u ϕb M n

“good”

“not good”

= flexural_strength “good”

Check beam deflections and available strength. Check the deflection of the beam under

construction considering only the weight of the concrete as contributing to the constructiondead load.

Limit the deflection to a maximum of 2.5 in to facilitate concrete placement (construction).

=≔ I req ―――――――⋅⋅5 Constructiondead Lbeam

4

⋅⋅384 E 2.5 in1056 in4

From Manual Table 3-20, a W21x50 has a Ix = 984, therefore this member doesn't satisfy thedeflection criteria under construction.

Using Manual Table 3-20 revise the trial secion to a W21x55 which has Ix = 1140 as noted in

parenthesis below the shape designation.

Check selected member strength as an unshored beam under construction loads assuming

adequate lateral bracing through the deck attachment to the beam flange.

Factored construction loads:




=≔C1 ⋅1.4 Constructiondead 1.16 ―ip

ft

=≔C2 +⋅1.2 Constructiondead ⋅1.6 Constructionlive 1.32kip

ft

=≔C max C1 C2 1.32 ―ipft

=≔ M u.unshored ――⋅C Lbeam

2

8333 ⋅ip ft

≔ϕb M px ⋅473 kip ft [AISC, Table 3-2, p. 3-17]

≔ flexural_strength ||||||

if

else

≤ M u.unshored ϕb M px

“good”

“not good”


For a W21x55 with Y2 = 7 in, the member has sufficient available strength when PNA is atlocation 6 and Qn = 292 kips. Manual Table 3-19, p. 3-177 and Manual Table 3-20, p. 3-200.

≔ϕb M n ⋅756 kip ft [AISC, Table 3-19, p. 3-177]

≔ flexural_strength ||||||

if

else

≤ M u ϕb M n

“good”

“not good”


Check "a":

≔ ΣQn 292 kip

=≔a ――― ΣQn

⋅⋅0.85 f`c beff

0.716 in




≔check_a ||||||

if

else

≤a atrial

“good”

“not good”


Check live load deflection:

=≔ΔLL.allowable ―Lbeam

3601.5 in

A lower bound moment of inertia for composite beams is tabulated in Manual Table 3-20.

For a W21x55 with Y2 = 7 in and the PNA at location 6, Ilb = 2440.

≔ I LB 2440 in4

[AISC, Table 3-20, p. 3-200]

=≔ΔLL ―――⋅⋅5 Live Lbeam

4

⋅⋅384 E I LB

1.3 in

≔deflection ||||

||

if

else

≤ΔLL ΔLL.allowable

“good”

“not good”

=deflection “good”

Determine if the beam has sufficient available shear strength:

=≔V u ⋅―Lbeam

2wu 61 kip

≔ϕvV nx 234 kip [AISC, Table 3-2, p. 3-17]

≔shear ||||||

if

else

≤V u ϕvV nx

“good”

“not good”

=shear “good”




Determine the required number of shear studs:

Using perpendicular deck with one 0.75 in diameter weak stud per rib in normal 4 ksiconcrete, Qn = 17.2 kip/stud.

≔dstud 0.75 in

≔Qn 17.2 kip [AISC, Table 3-21, p. 3-207]

=≔Studs ― ΣQn

Qn

17 (on each side of the beam)

Total number of shear connectors; use 2(17) = 34 shear connectors

Check the spacing of the shear connectors:

≔stud_spacing if

else

<<⋅6 dstud 12 in ⋅8 tslab

“good”

“not good”

=stud_spacing “good”

The studs are to be 5 in long so that they will extend a minimum of 1.5 in into the slab.

example i-1.pdf

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