Project Lead The Way, Inc.
Copyright 2010
CEA
–
Unit 3
–
Lesson 3.2
–
Activity 3.2.6
–
Beam Design
–
Page
1
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 dict
ated by building codes and standards and require the
in
clusion of a factor of safety.
Therefore, the beam design selected must possess
more strength than required to resist the imposed loads.
In this activity you will design floor framing (beams and girde
rs) for a hotel.
Equipment
Pencil
Calculator
Computer with internet access
Website:
http://www.structural

drafting

net

expert.com/
Activity 3.2.
4
Beam Analysis Short Cuts
(completed)
MD
Solids software
Procedure
The PARTIAL SECOND FLOOR FRAMING PLAN
for a new hotel
is given below.
The second floor will be used for conference space. Design the following floor
framing members for the hotel structure.
Interior beam
Exterior beam
Girder on C
olumn Line 3
Girder on Column Line 5
Project Lead The Way, Inc.
Copyright 2010
CEA
–
Unit 3
–
Lesson 3.2
–
Activity 3.2.6
–
Beam Design
–
Page
2
Criteria
The following data is to be used
for design of the floor framing:
Dead
l
oad =
50 psf
Assume the weight of the floor beams and girders are included in the
d
ead
l
oad.
Floor
l
ive
l
oad
=
100 psf (
Hotels
–
Publ
ic Space per IBC 2009 Table 1607.1)
F
y
=
50
,000 psi
The floor will support a plaster ceiling
.
Note: E = 29,000,000 psi for structural steel
1.
Complete the following for each beam and girder
using the Allowable Strength
Design method.
You must
show all work
and include proper
units
for full credit.
Calculate the loading
Create a beam diagram
Calculate end r
eactions
Calculate the maximum moment
Calculate
the
required
nominal moment
Calculate required plastic section modulus
Choose an efficient steel wide
flange to safely carry the load
Check shear capacity
Calculate deflection limits
Check
d
eflection
using beam formula
; if
necessary, revise member
choice and recalculate deflection
Choose final design
; p
rove that the revised choice is sufficient to carry
be
nding moment and shear
Project Lead The Way, Inc.
Copyright 2010
CEA
–
Unit 3
–
Lesson 3.2
–
Activity 3.2.6
–
Beam Design
–
Page
3
2.
C
heck
calculations for each beam
and girder
using MD Solids.
Print out the
following:
Shear and
m
oment diagrams
Slope and
d
eflection (in inches) diagrams
Note:
Be sure to choose your final beam designation in MD Solids before
produ
cing slope an
d
deflection diagrams since these values
are
depend
ent
up
on
the
s
ection properties of the beam.
Use
inches for the units on the deflection
diagram.
Conclusions
1.
If the beam loading and beam span is different for every beam in a building, is it
reasonable
and practical
to choose a different beam section for every
installation? Why or why not?
Yes, technically it would be cheaper to use different sized beams depending
on what they will hold up. However, realistically, it would be much easier to
a
ssign one beam size per area.
2.
Aside from simply pushing the wrong keys on your calculator, what is the most
likely reason for an error in calculating a required section modulus or a
deflection?
Looking up wrong values on the chart.
3.
Which structural steel
section would carry the largest bending moment, a W12 x
22 or a W14 x 22? Why? If subjected to the same magnitude of loading over the
same span, which beam would display the largest deflection? Why?
The W14x22 because of its longer length.
Project Lead The Way, Inc.
Copyright 2010
CEA
–
Unit 3
–
Lesson 3.2
–
Activity 3.2.6
–
Beam Design
–
Page
4
Interior Beam
1.
Include the l
oading and
b
eam
d
iagram
s.
1000 plf
2.
Calculate the
e
nd
r
eaction and
m
aximum
m
oment
.
40,500 ft(lb)
3.
Calculate the
r
equired
n
ominal
m
oment
.
67,635 ft(lb)
4.
Determine
the
required plastic section modulus and select an efficient wide
flange.
W12X14
Z
X
=17.4 in
3
l
x
= 88.6 in
4
T
w
= 0.2 in
d= 11.91 in
5.
Check
the
shear strength.
ITS
GOOOOOOOOD
6.
Calculate
d
eflection
l
imits
.
0.6 in
7.
Calculate
a
ctual
d
eflections
.
0.92 in > 0.9 in
NOT
GOOOOOOOOD
8.
S
elect a final design.
Use W12x16
Project Lead The Way, Inc.
Copyright 2010
CEA
–
Unit 3
–
Lesson 3.2
–
Activity 3.2.6
–
Beam Design
–
Page
5
E
xterior
Beam
1.
Include the l
oading and
b
eam
d
iagram
s.
500 plf
2.
Calculate the
e
nd
r
eaction and
m
aximum
m
oment
.
20,250 ft(lb)
3.
Calculate the
r
equired
n
ominal
m
oment
.
33,818 ft(lb)
4.
Determine
the
required plastic section modulus and select an efficient wide
flange.
W1
0x
12
Z
x
= 12.6 in.
3
I
x
= 53.8 in.
4
d = 9.87 in. t
w
= 0.19 in.
5.
Check
the
shear strength.
ITS
GOOOOOOOOD
6.
Calculate
d
eflection
l
imits
.
0.9 in, 0.6 in
7.
Calculate
a
ctual
d
eflections
.
0.6 in
8.
S
elect a final design.
W10x12
Project Lead The Way, Inc.
Copyright 2010
CEA
–
Unit 3
–
Lesson 3.2
–
Activity 3.2.6
–
Beam Design
–
Page
6
Girder on Column Line 3
1.
Include the l
oading and
b
eam
d
iagram
s.
18,000 lb
2.
Calculate the
e
nd
r
eaction and
m
aximum
m
oment
.
200,060 ft(lb)
3.
Calculate the
r
equired
n
ominal
m
oment
.
200,500 ft(lb)
4.
Determine
the
required plastic section modulus and select an efficient wide
flange.
W16x31
Z
x
=54.0 in.
3
I
x
= 375 in.
4
d = 15.88 in. t
w
= 0.275 in.
5.
Check
the
shear strength.
131,010 > 27,000
ITS
GOOOOOOOOD
6.
Calculate
d
eflection
l
imits
.
1 in, 0.67 in
7.
Calculate
a
ctual
d
eflections
0.54 in < 0.67 in
ITS
GOOOOOOOOD
8.
S
elect a final design.
Use W16 x 31
Project Lead The Way, Inc.
Copyright 2010
CEA
–
Unit 3
–
Lesson 3.2
–
Activity 3.2.6
–
Beam Design
–
Page
7
Girder on Column Line 5
1.
Include the l
oading and
b
eam
d
iagram
s.
9000 lb
2.
Calculate the
e
nd
r
eaction and
m
aximum
m
oment
.
60,030 ft(lb)
3.
Calculate the
r
equired
n
ominal
m
oment
.
100,250 ft(lb)
4.
Determine
the
required plastic section modulus and select an efficient wide
flange.
24.06 in
5.
Check
the
shear strength.
85,728 lb > 13,500 lb
ITS
GOOOOOOOOD
6.
Calculate
d
eflection
l
imits
.
1 in, 0.67 in
7.
Calculate
a
ctual
d
eflections
.
1.17 in > 1 in
NOT
GOOOOOOOOD
0.51
in < 0.67 in
ITS
GOOOOOOOOD
8.
S
elect a final design
W14x22
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