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HW 5 Flexural Behavior and Design

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CEES 4753 HW #5
Assigned 10/3/19
Initial Canvas Submission Due 10/24/19 @ 3:00 pm
Final Self-Assessed Submission 10/29/19 @ 3:00 pm
For all problems you may assume dry-service conditions, normal temperatures, and bending
about the strong axis unless otherwise specified.
1. Breyer 6.1. A simply supported wood roof beam is loaded with single point dead and roof
live loads applied at midspan (PD = 400 lb, PLr = 1600 lb) of an 8 ft span. The controlling
load combinations are D + Lr (ASD) and 1.2D + 1.6Lr (LRFD). A No. 1 DF-L 4 x 8 is used
for the beam and it is continuously braced (lu = 0). The allowable live load deflection is Δ ≤
L/360. Determine whether the beam is adequate for ASD and LRFD by determining:
a. Size Category (Dimension lumber, B&S, P&T)
b. Reference design values: Fb, Fv, and E
c. Adjusted ASD values: F’b, F’v, and E’
d. Actual stresses (ASD) and deflection: fb, fv, and Δ
e. Compare the actual stresses and adjusted design values, and determine if the
member is adequate (ASD)
f. Nominal LRFD values Fbn, Fvn, and E
g. Adjusted LRFD values F’bn, F’vn, and E’
h. Adjusted LRFD moment and shear resistances: M’n and V’n
i. Factored moment and shear (LRFD), and actual deflection: Mu, Vu, and Δ
j. Determine if the member is adequate using LRFD
2. Breyer 6.4. Use your hand solution to Problem 1 to create a computer template (Excel,
MatCAD, MATLAB, etc.) to solve similar problems using ASD and LRFD. Expand the
template from the conditions in Problem 1 to include: MC > 19%, any span length L, any
magnitude load P or Pu, any magnitude uniformly distributed load, any unbraced length lu,
and any sawn lumber trial member size. Use the results of problem 1 to ensure that your
spreadsheet works.
3. Breyer 6.22. A series of simply supported, closely spaced floor beams are to be designed.
They are loaded with a uniformly distributed dead load qD = 18 psf and live load qL = 50 psf.
The controlling load combination is 1.2D + 1.6L (LRFD). The span length is 15 ft, the
members will be spaced at 16 in. o.c., and the members have continuous lateral support. No.
1 Hem-Fir will be used for all members. Allowable live load deflection is ΔL ≤ L/360 and
allowable deflection for total load is Δ(D+L) ≤ L/240. Determine required minimum beam size.
Give all items required for LRFD in Problem 1 as part of the solution.
4. Breyer 6.23. For the beam designed in problem 3, determine the size of notches allowed by
the NDS on both the tension and compression side at (a) the supports or ends of the member
and (b) in the interior of the span. Determine the shear capacity at the support, if a 1 in. deep
notch were assumed at the support using ASD procedures.
CEES 4753 HW #5
Assigned 10/3/19
Initial Canvas Submission Due 10/24/19 @ 3:00 pm
Final Self-Assessed Submission 10/29/19 @ 3:00 pm
5. Breyer 6.27. The roof rafters shown are 24 in. o.c. The roof dead load is 15 psf along the
roof, and the design snow load is 50 psf. Calculate the design shear and moment, using the
horizontal plane method of Example 2.6 (see Fig. 2.6b). Disregard deflection, lateral stability
is not a problem, and lumber is No. 1 DF-L. Determine the required minimum rafter size.
Give all items required for Problem 1 for ASD as part of the solution.
14 ft
12
4
6x Ridge Beam
Neglect
Overhang
Rafter
2 x 4 Stud Wall
6. Breyer 6.29. A simply supported beam with a span of 24 ft has the compression side
supported laterally at the ends and the quarter points. The member is a resawn 2 ½ x 19 ½ DF
24F-1.8E glulam. The load is a combination of D + L (ASD). Determine:
a. the maximum allowable moment Mmax in ft-k and the corresponding maximum
factored load Pmax in kips (ASD) that the beam can support at mid-span based on
bending.
CEES 4753 HW #5
Assigned 10/3/19
Initial Canvas Submission Due 10/24/19 @ 3:00 pm
Final Self-Assessed Submission 10/29/19 @ 3:00 pm
7. Breyer 6.31. The rafter connection shown is loaded with a load combination of PD = 140 lb,
and Ps = 560 lb. Consider the D + S (ASD) or 1.2D + 1.6S (LRFD) load combination.
Lumber is No. 1 Spruce-Pine-Fir (South). Determine:
a. The actual bearing stress fc┴ in the rafter and in the top plate of the wall (ASD).
b. The adjusted ASD bearing value F’c┴ in the top plate
c. The adjusted ASD bearing value F’cθ in the rafter
d. Factored bearing load Pu in the rafter and in the top plate of the wall (LRFD)
e. The adjusted LRFD bearing resistance P’n┴ in the top plate
f. The adjusted LRFD bearing resistance P’nθ in the rafter
P
12
6
2 x 10 Rafter
Top Plate
2 x 4 Stud Wall