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Bending Moments and Shear Forces in a Beam and Parallel Chord Truss, Exercises of Structural Design and Architecture

Alagappa UniversityStructural Design and Architecture

The solution to three engineering problems related to bending moments and shear forces in a beam and a parallel chord truss. The problems involve calculating the moment diagram, moment of inertia, maximum bending stress, maximum shear stress, deflection, number of bolts required for shear, bearing force, minimum weld size, member forces using the method of joints and sections, minimum area required for a member, stress value and type, critical value of fce, and the allowable buckling load. The document also includes diagrams and specifications for the beam and truss.

Typology: Exercises

2011/2012

Uploaded on 12/22/2012

bageshri
bageshri 🇮🇳

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bg1
Figure 1d. (elevation)
Figure 1b.
V
M
A
wD = 2300 lb/ft
wL = 2650 lb/ft
2 ft 10 ft
x
x
Figure 1a.
23.9 k
43.4 k
-6.1 k
Figure 1c.
5 in
6.56 in
x x
8.5” x 1.5”plate
5”
φ
semicircle
fillet weld
to column
angles with n
bolts through
stem
B
column flange
Figure 1e. (plan)
fillet weld
to column
angles with
n bolts through
stem
column
C
14 k
PL = 30 k PD = 14 k
Figure 1f.
Practice Final Examination
Problem 1) Worth 45%
• A 12 ft beam with live and dead loading is shown in Figure 1a.
• The cross section geometry of the beam is shown in Figure 1c.
• The material is Giggium steel with E = 32,000 ksi,
Fb = 60 ksi, Fv = 35 ksi, Fy = 45 ksi, and Fu = 65 ksi.
• The beam end connection is detailed in Figures 1d and 1e. The
angle legs are 3/8” thick, with 7/8 in diameter bolts of A325-N
and standard holes.
• The weld material is E70XX.
FIND:
a) The completed bending moment diagram in
Figure 1b, and Mmax.
b) The moment of inertia for the cross section by
completing the chart of Figure 1f.
c) The maximum bending stress in the beam.
d) The maximum shear stress in the beam.
e) The deflection at the free end D due to live load
only.
f) The number of bolts required for shear at the
beam shear connection at end A.
g) The bearing force allowed at the beam shear
connection when 4 bolts are used.
h) The minimum weld size required for shear for the
angles to the colu mn if the length on each angle
is 3.5 in.
A (in2) Ix (in4) dy (in) Ady2 (in3)
semicircle
web 12.75 76.77 2.31 68.04
a) b) 248.5 in4 c)
d) 3.7 ksi e) -1.33 in (up) f) 2 bolts (1.7 required)
g) 204.9 k h)
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pf2

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Download Bending Moments and Shear Forces in a Beam and Parallel Chord Truss and more Exercises Structural Design and Architecture in PDF only on Docsity!

Figure 1d. (elevation)

Figure 1b.

V

M

A

wD = 2300 lb/ft

wL = 2650 lb/ft

10 ft 2 ft

x

x

Figure 1a.

23.9 k

43.4 k

-6.1 k

Figure 1c.

5 in

6.56 in

x x 8.5” x 1.5”plate

5” φ semicircle

fillet weld to column

angles with n bolts through stem

B

column flange

Figure 1e. (plan)

fillet weld to column

angles with n bolts through stem

column

C

14 k

PL = 30 k PD = 14 k

Figure 1f.

Practice Final Examination

Problem 1) Worth 45%

  • A 12 ft beam with live and dead loading is shown in Figure 1a.
  • The cross section geometry of the beam is shown in Figure 1c.
  • The material is Giggium steel with E = 32,000 ksi, F (^) b = 60 ksi, Fv = 35 ksi, F (^) y = 45 ksi, and F (^) u = 65 ksi.
  • The beam end connection is detailed in Figures 1d and 1e. The angle legs are 3/8” thick, with 7/8 in diameter bolts of A325-N and standard holes.
  • The weld material is E70XX.

FIND:

a) The completed bending moment diagram in Figure 1b, and Mma x.

b) The moment of inertia for the cross section by completing the chart of Figure 1f.

c) The maximum bending stress in the beam.

d) The maximum shear stress in the beam.

e) The deflection at the free end D due to live load only.

f) The number of bolts required for shear at the beam shear connection at end A.

g) The bearing force allowed at the beam shear connection when 4 bolts are used.

h) The minimum weld size required for shear for the angles to the colu mn if th e length on each angle is 3.5 in. A (in^2 ) I (^) x (in^4 ) dy (in) Ady^2 (in^3 ) semicircle web 12.75 76.77 2.31 68.

a) b) 248.5 in 4 c)

d) 3.7 ksi e) -1.33 in (up) f) 2 bolts (1.7 required)

g) 204.9 k h)

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gure 2b.

B

G

Figure 2a.

H F

A

C

35 ° E

n bolts

D

200 lb

600 lb

800 lb

100 lb

4 @ 9 ft = 36 ft

6 in

B C

6 ft-8 in.

Figure 2c. (top view of bracing)

D

5 ft ft 6 ft-4 in.

bracing

Problem 2) Worth 45%

  • A parallel chord truss is shown in the Figure 2a has the following support reactions: A (^) x = 100 lb, A (^) y = 267.5 lb, E =-267.5 lb.
  • Wind load is considered.
  • The truss is constructed with glu-lam lumber having E =1.85 x 10^6 psi, α = 3.8 x 10 -6^ /°F, Fc = 1700 psi ( no adjustment factors applied), allowable tension stress F’ (^) t = 1200 psi (adjustment factors applied), and allowable bearing stress F’ (^) p = 650 psi (adjustment factors applied).
  • The truss members are 3.125 in. x 6 in. with I (^) x = 56.25 in 4 , and Iy = 15.25 in^4.
  • The bottom chord that is continuous the length of the truss is connected as shown in Figure 2b.
  • The top chord that is continuous is laterally braced at each end and across the span as show in Figure 2c. The ends are considered to be pinned.

FIND:

i) The member forces in AB and AH using the method of joints.

j) The member forces in BG and BC using the method of sections.

k) The minimum area required for member HG if the tension force is 6.3 kips.

l) The stress value and type in member AB resulting from a temperature decrease of 15° F (with no loading) if the member can only shorten by 0.003 inches.

m) The critical value of FCE for the upper chord and the ratio used to find C (^) p.

n) The allowable buckling load for the lower chord if Cp has been determined to be 0.403 for the weak axis and 0.214 for the strong axis.

o) The minimum number of 5/8 in. diameter bolts required and their arrangement for the connection shown in Figure 2b if the maximum tension force in either member is 7.5 kips and the bolt holes are ¾” in diameter.

j) j) k)

l) 63.3 psi in tension m)^ n) 10.9 k

o) 6 bolts in 2 rows of 3 (≤ 5.3 net tension & ≥ 5.9 bearing)

Problem 3) Worth 10% (conceptual questions)

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