Activity 3.2.6 Beam Design Introduction Beam design is based on four important considerations: bending moment, shear, deflection, and cost. Once the design loads have been determined and the beam has been analyzed to determine the resulting internal shear forces and bending moments imposed, a structural engineer can select a cost-effective beam design that will provide sufficient shear and bending strength and adequate stiffness to limit deflection to acceptable limits. Beam design methods are dictated by building codes and standards and require the inclusion of a factor of safety. Therefore, the beam design selected must possess more strength than required to resist the imposed loads. n this activity you will design floor framing !beams and girders" for a hotel.
Equipment • • • • • •
#encil $alculator $omputer with nternet access %ebsite: http://www.structura!dra"ting!net!e#pert.com/ &ctivity '.(.) '.(.) Beam Beam &nalysis &nalysis *hort *hort $uts $uts !completed" !completed" + *olids software
$rocedure The #artial *econd loor raming #lan for a new hotel is given below. The second floor will be used for conference space. esign the following floor framing members for the hotel structure. nterior beam /terior beam 0irder on column line ' 0irder on column line 1 • • • •
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age 4
%riteria The following data is to be used for design of the floor framing: ead load 9 13 psf &ssume the the weight weight of the floor beams beams and girders girders are are included included in the dead dead load load loor live load 9 433 psf !otels8#ublic space per B$ table 473;.4" y 9 13,333 psi The floor will support a plaster ceiling
• • • • •
4. $omplete the the following following for each beam beam and girder girder using the the &llowable &llowable *trength *trength esign method. >ou must show all wor? and include proper units for full credit. • • • • • • • • • •
•
$alculate the loading $reate a beam diagram $alculate end reactions $alculate the ma/imum moment $alculate the required nominal moment $alculate required plastic section modulus $hoose an efficient steel wide flange to safely carry the load $hec? shear capacity $alculate deflection limits $hec? deflection using beam formula@ if necessary, revise member choice and recalculate deflection $hoose final design@ prove that the revised choice is sufficient to carry bending moment and shear
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age (
Interior Beam 4 nclud nclude e the the load loading ing and and beam beam diag diagram rams. s. .
&impe Beam! 'ni"ormy Distri(uted )oads *D) + ,- (/"t 2 ,6.60 "t + 333.- p" *)) + ,1 (/"t 2 ,6.60 "t + 666.60 p" * + *D) *)) + 333.- 666.60 + 1.10 p" + 1 p" (. $alculat $alculate e the end end reaction reaction and and ma/imum ma/imum moment moment.. 4+
ωL
+
2
2
+
ωL 8
+
1,000 (18 ft )
+
2 1,000 ( 18
2
)
8
18,000
+
+ 5 (
2
1,000 ( 324 ) 8
+
324,000 8
+ 7- "t8(
'. $alculat $alculate e the required required nominal nominal mome moment. nt. n ≥ a9( + ,7- "t8(,1.60 + 6063- "t8( ). etermine the required required plastic plastic section section modulus modulus and select select an efficien efficientt wide flange. n + y;# + ;#
≥ ,6063- "t8( ,12in/ 1 "t / - ,(/in2 + 16.2327
*1#10 ;# + 1<.0 in3 I# + <1.5 in7 d + 1.11 in tw + .27 in 1. $hec $hec? ? the the shear shear stren strength gth.. =n ≥ =a9v ≥ ,5 (,1.- + 13- ( =n + .6ydtw + .6,-,(/in2,1.11 in,.27 in,.27 in + 02052 ( >ood
≥ 13- (
7. $alcu $alculat late e deflect deflection ion limit limits. s. ?D))) @ )/27 + ,1< "t,12in/1"t / 27 + .5 ?)) @ )/36 + ,1<"t8 ,12 in/1"t/ 36 + .6 in ;. $alculat $alculate e actual actual deflecti deflections ons..
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age '
12 ∈ ¿ 12 ∈
A666 9
5w L
1 ft
18 ft ∗¿
4
384 EI
¿
4
¿ lb ∗1 ft
9
ft
1,000
5¿
9 3.== in
¿ 0 . 9 ∈ ¿
¿
¿
¿ 12 ∈ ¿ ¿ 12 ∈
1 ft
A66 9
5w L
18 ft ∗¿
4
384 EI
4
¿
9 666.67
lb ∗1 ft ft 5¿
¿
9 3.77 in
¿ 0 . 6 ∈ ¿
¿
¿
C.
*elect a final design.
*1#15
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age )
E#terior Beam 4 nclud nclude e the the load loading ing and and beam beam diag diagram rams. s.
&impe Beam! 'ni"ormy Distri(uted )oads *D) + ,- (/"t 2 ,3.33 "t + 166.-- (/"t + 166.- p" *)) + ,1 (/"t 2 ,3.33 "t + 333.33 (/"t + 333 p" * + *D) *)) + 166.- p" 333 p" + 755.- p" ,- p"
=. $alculat $alculate e the end end reaction reaction and and ma/imum ma/imum moment moment.. 4 + w)/2 + ,,- (/"t,1< "t /2 + 5/2 + 7- ( + w)2 /< + ,,- (/"t,1< (/"t,1< 2 "t /< + 22- "t8(
43.$alculat 43. $alculate e the required nominal nominal moment. n ≥ a9( + ,22- "t8(,1.60 + 33<1< "t8( 44. etermine the required plastic section modulus and select an efficient wide flange. n + y;# + ;# ≥ ,33<1< "t8( # ,12in./1"t / ,- (/in 2 + <.1 in3 *1#12 ;# + 12.6 in3 I# + -3.< in 7 d + 5.<0 in tw + .15 in 4(.$hec? 4(. $hec? the shear strength. strength. =n ≥ =a9v ≥ ,7- (,1.- + 60- ( =n + .6ydtw + .6,- (/in 2,5.<0 in,.15 in + -62-5 ( >ood
≥ 60- (s
4'.$alculat 4'. $alculate e deflection limits. ?D))) @ )/27 + ,1<"t 8 ,12 in/1"t/ 27 + .5 in ?)) @ )/36 + ,1<"t8 ,12 in/1"t/ 36 + .6 in 4).$alculat 4). $alculate e actual deflections. deflections.
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age 1
12 ∈ ¿ 12 ∈ 5w L
?D))) +
1 ft
18 ft ∗¿
4
384 EI
¿
4
¿ lb ∗1 ft
+ 500
ft
+ .06 in
¿ 0.9 ∈ ¿ >ood
¿
¿ 5¿ ¿ 12 ∈ ¿ ¿ 12 ∈ 1 ft
?)) +
5w L
18 ft ∗¿
4
384 EI
¿
+ 333
41.
4
lb ∗1 ft ft
¿ 5¿ ¿
+ .- in
¿ 0.6 ∈ ¿ >ood
¿
*elect a final design.
*1#12
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age 7
>irder on %oumn )ine 3 4 nclud nclude e the the load loading ing and and beam beam diag diagram rams. s.
&impe Beam wo wo Equa %oncentrated )oads &ymmetricay $aced and 'ni"ormy Distri(uted )oad $ + 5 ( "rom e"t 5 "rom right + 1< ( 47.$alculat 47. $alculate e the end reaction and ma/imum moment. 4 + $ + 1<( + $a + ,1<(,6.60"t + 126 "t8( 4;.$alculat 4;. $alculate e the required nominal nominal moment. n ≥ a9( + ,126 "t8(,1.60 + 2- "t8( 4C.etermine the required plastic section modulus and select an efficient wide flange. n + y;# + ;# ≥ ,2- "t8(,12in/1"t / ,- (/in 2 + -<.12 in3 *16#31 ;# + -7 in3 I# + 30- in7 d + 1-.<< in tw + .20- in 4=.$hec? 4=. $hec? the shear strength. strength. =n
≥ =a9v ¿ ,1< (,1.- + 20 (
=n + .6ydtw + .6,- (/in 2,1-.<< in,.20- in + 1311 >ood
≥ 20
(3.$alculat (3. $alculate e deflection limits. ?D))) @ )/27 + ,2"t 8 ,12 in/1"t/ 27 + 1 in ?)) @ )/36 + ,2"t 8 ,12 in / 36 + .60 in (4.$alculat (4. $alculate e actual deflections. deflections.
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age ;
12 ∈
¿ 1 ft
6.67 ft ∗¿
¿
29,000,000
lb
¿3
¿ ¿ ¿2 12 ∈ 1 ft 6.66 ¿ =¿
?D))) + ,$a/27EI,3)2 7a2 +
12 ∈
.<1
¿
1 >ood
¿ ¿ 2−4 ¿
1 ft 20 ft ¿ 3¿ 24 ¿ ( 18,000 lb ) ¿
¿
?)) + 66.60C ?D))) + .660,.<1+ .-7
((.
¿ .60 in >ood
*elect a final design.
*16#31
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age C
>irder on %oumn )ine 4 nclud nclude e the the load loading ing and and beam beam diag diagram rams. s.
&impe Beam wo wo Equa %oncentrated )oads &ymmetricay $aced $ + 7- ( "rom e"t 7- ( "rom right + 5 ( ('.$alculat ('. $alculate e the end reaction and ma/imum moment. 4 + $ + 5 ( + $a + ,5 (,6.60 "t + 63 "t8( ().$alculat (). $alculate e the required nominal nominal moment. n ≥ a9( + ,63 "t8(,1.60 + 12- "t8( (1.etermine the required plastic section modulus and select an efficient wide flange. n + y;# + ;# ≥ ,12- "t8(,12in/1"t / ,- (/in 2 +27.6 in 3 *12#15 ;# + 27.0 in3 I# + 13 in 7 d + 12.16 in tw + .23- in (7.$hec? (7. $hec? the shear strength. strength. =n
≥ =a9v ¿ ,5 (,1.- + 13- (
=n + .6ydtw + .6,- (/in 2,12.16 in,.23- in + <-02<( 13- ( >ood (;.$alculat (;. $alculate e deflection limits. ?D))) @ )/27 + ,2"t 8 ,12 in/1"t/ 27 + 1 in ?)) @ )/36 + ,2"t 8 ,12 in / 36 + .60 in (C.$alculat (C. $alculate e actual deflections. deflections.
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age =
12 ∈
¿ 1 ft
6 . 67 ft ∗¿
¿
29 , 000 , 000
A666 9 !#aD()"!'6( E )a(" 9
lb
¿ ¿ ¿2 12∈
¿3
1 ft 6 . 66 ¿ =¿
12 ∈
4.4;
¿
4
¿ ¿ 2− 4 ¿
1 ft 20 ft ¿ 3¿ 24 ¿ ( 9 , 000 lb ) ¿
¿
(=.*elect (=. *elect a final design design *17#22
2 (343 #ro5ect 6ead The %ay, nc. $ivil ngineering and &rchitecture &ctivity '.(.7 Beam esign8#age 43
