Check the strength of each type of member in the one story steel frame building below.

Transcription

1 CE 33, Fall 200 Aalysis of Steel Baced Fame Bldg / 7 Chec the stegth of each type of membe the oe stoy steel fame buildg below. A 8 B 20 f 2 25 Side Elevatio 3 4 Pla View 32 F y 50 si all membes F u 65 si Fot Elevatio 20 Puls Gides Colums X Bacg Shape Z2x40 W2x44 W6x36 L2x2x/8 A g Loads: 3.5 thic light weight cocete slab (uit weight 20 pcf) LL 40 p WL 30 p Load Combatios:.2D +.6L.2D +.6L

2 CE 33, Fall 200 Aalysis of Steel Baced Fame Bldg 2 / 7 Idetify joists ad gides. The oof dec is suppoted by the Z shaped puls, which u tasvese to the dec cougatios (see exploded buildg figue below). The puls ae tu suppoted by the gides, which u tasvese to the puls. The gides ae suppoted at thei eds by the colums. A 8 w tib joist B Fist of all, the H shaped symbols epeset the colums I the Pla View at le, we see that some of the vetical membes the setch ae attached diectly to colums, but that some of the vetical membes ae attached at thei eds to othe beams. 3 The eds of the hoizotal membes, o the othe had, all attach to colums. 4 Pla View Theefoe, the hoizotal membes the setch ae gides, ad the vetical membes ae puls (if suppotg a oof) o joists (if suppotg a floo).

3 CE 33, Fall 200 Aalysis of Steel Baced Fame Bldg 3 / 7 Pul o Joist max M u Puls o joists ae fequetly cotuous beams ove seveal spas ( this example, the puls ae cotuous ove thee 25 foot spas). Loadg all of the spas of a cotuous beam may ot cause the maximum bedg momet. Although the positio of dead load is give, the positio of live load is vaiable ad the stuctual egee must deteme the loadg causg the maximum bedg momet. Oe way of detemg the loadg causg the maximum bedg momet is to apply all possible load cofiguatios, oe at a time, ad select the loadg causg the maximum effect. I this class, we will assume that the locatio of the maximum bedg momet due to dead plus live loads is the locatio with the maximum bedg momet due to dead loads. Locatio of max M D+L Locatio of max M D This is the case fo cotuous beams with equal spa legths. T Ou pocedue fo calculatg the maximum momet due to factoed loads will be:. Apply the dead load to all spas ad calculate the momet (M D ) usg chats fom the AISC maual 2. Assume that the locatio of the max M D+L the locatio of the max M D. Daw the fluece diagam fo momet fo this locatio. 3. Apply the live load to the spas dicated by the fluece diagam ad calculate the momet (M L ) usg the AISC chats. 4. Calculate M u fom.2 M D +.6 M L. Example. Dead Loads: Weight of slab 3.5 /2 / x 20pcf 35 p width of slab suppoted by joist tibutay width w tib 8 (see setch o bottom of Pg. 2) uifom load due to weight of slab w slab w slab 35 p x lf self weight of joist 40 plf uifom load due to self weight of joist w SW 40 plf 25 w D uifom load due to all dead loads w D w D lf + 40 plf /000 lb/ lf M D, 0.080wL wL 2 Max M D 0.00 wl 2 fom AISC chats M D 0.00 (0.320 lf )(25 ) 2 M D wL

4 CE 33, Fall 200 Aalysis of Steel Baced Fame Bldg 4 / 7 Live Loads: Assume A T aea suppoted by oe spa of joist (cosevative) 5 LL 0.25 eductio +, 0.4 LL.0 eductio LL AT 2 ( beams) A LL T LL tibutayaeaof joist (8 eductio (2)(200 )(25 ) ) Theefoe educed live load L ed 40 p x.0 40 p w Led (40.0 p )(8 )/(000 lb/ ) lf Assume max M D+L occus at locatio of max M D tibutay width fo joist (see setch o bottom of Page 2) Ifluece Diagam fo M at Suppot 2: Spa loadg to cause max. M at Suppot 2: w LL max M L 0.67(0.320 lf )(25 ) M LL.2( 20.0 ) +.6( 23.3 ) max M u wL max M u Joist uity chec L b_comp_flage 0 < L p (assume compessio flage is baced full legth by oof diaphagm). Theefoe, calculate φ M φ M p φ M p 24, [AISC Table 3 2, pg 54 FE Ref.] M u 6.3 U. C <.0, φ M 24 OK

5 CE 33, Fall 200 Aalysis of Steel Baced Fame Bldg 5 / 7 Gide max M u Sce all gides ae the same size, the gide with the lagest uity chec will be the gide with the lagest loads. Theefoe, aalyze a gide fom a teio fame. The loads o this gide ae dicated the setch below, whee P ext the loads o the gide fom exteio joists ad P t the loads o the gide fom teio joists 8 P ext P t P t P t P ext 8 A tib fo load o gide fom exteio joist 25 The tibutay aeas used to calculate these loads ae show the setch at ight. wt slab 35 p wt joists 40 plf wt gide 44 plf Cocetated load due to dead load at a teio joists P D t P D t (35 p )(25 )(8 ) + (40 plf )(25 ) + (44 plf )(8 ) 8.35 Sce the gide is a sgle spa, thee is o eed to coside spa load pattes fo live load. Fo live load eductio, tibutay aea (A t ) equals tibutay width (25 ) times spa legth (32 ) A t 25 x LL eductio (betwee (2)(800 ) 0.4 ad.0, OK) P L 27 t (40p )(0.625)(25 )(8 ) P u_t.2(8.35 ) +.6(5.0 ) 8.0 Ae dawg the shea ad momet diagams (at ight), M u 288 A tib fo load o gide fom teio joist V M

6 CE 33, Fall 200 Aalysis of Steel Baced Fame Bldg 6 / 7 Gide uity chec L p 4.45, L 3.0 [AISC Table 3 2, pg 54 FE Ref.] L p < (L b 8 ) < L φ M C b [φ M p BF(L b L p )] < φ M p C b.0 (always fo this class) φ M p 358 [AISC Table 3 2, pg 54 FE Ref.] BF 6.8 [AISC Table 3 2, pg 54 FE Ref.] φ M () [ ( ] [pg 50, FE Ref.] φ M 298 (< 358 φ M p ) UC M u φ M <, OK Colum max P u (citical colum teio colum) SDL 35 p wt joists 40 plf wt gide 44 plf P D (35 p )(25 )(6 ) + (40 plf )(25 )(5 joists /2) + (44 plf )(6 ) P D 7.2 A t (32'/2) (25 ) 400 LL eductio (4) (400 ) P L (40 p )(0.625)(400 ) 0.0 P u.2(7.2 ) +.6(0.0 ) 36.6 Colum uity chec A 0.6 x y L L u _ x x u _ y y 2, x 6.5 (.0)( (.0)( , y.52 ) 36.9 ) 78.9 KL/ 79 (oud up) φ F c 28.5 si [AISC Table 4 22, pg 57 FE Ref.] φ P φ F c A (28.5 si ) (0.6 2 ) 302, [Table,pg 53 FE Refe] Pu 36.6 UC 0.2 <.0, OK (but ove desiged) φ P 302 cotols 6 25

7 CE 33, Fall 200 Aalysis of Steel Baced Fame Bldg 7 / 7 Ed Wall Coss Bacg max T u due to Wd Loads Half of wd load o log wall of buildg goes dow to goud, ad half goes up to the oof diaphagm. The wd load to the oof is esisted by x bacg the ed walls (40 foot wide walls). Theefoe the load to oe ed wall is W hcol Legth of Bldg 20' 75' P U ed wall (.6)( WL)( )( ) (.6)(30p )( )( ) Ed wall X bacg: T ed wall bace (8 )(37.7 / 32 ) T U ed wall bace P ed wall bace Ed Wall Coss Bacg φ T A g [Agles Popeties] φ A g F y 0.9 ( ) (50 si) 2.8 φ A e F u 0.75 (.0 x ) (65 si) 23.6 (assume U.0 fo this class) φ T 2.8 Tu 2.2 UC 0.97 <.0, OK φ T 2.8 cotols 8 C Pla View 8 C 2.2 T Elevatio View