CEE 454 HW #1 Solution
2.21. The enclosed building in the figure below is a two-story essential facility located near Denver, CO. Wind Exposure C applies.
a. The design wind pressures in both principal directions of the building for main windforce-resisting systems.
Sol.
** If you need the background for this problem, read Ch 2.9 and Ch 2.10.
** Essential eq: ps = ps30 * IW * λ (See p2.28 of textbook)
- V = 90 mph from IBC Fig 1609 for Denver, CO (Refer to C.12 of textbook)
- IW = 1.15 from IBC Table 1604.5 for essential facility (Refer to C.4)
- Ridge height =
- hmean = (22 + 28.25)/2 = 25.1 ft
- λ = 1.35 from IBC Table 1609.6.2.1(4) for Exposure C and hmean = 25.1 ft (Refer to C.23)
Based on IBC Table 1609.6.2.1(1) for roof slope 3:12,
Zone / Ps30 (psf) / ps = ps30 * IW * λA / 16.1 / 25.0
B / -5.4 / -8.4
C / 10.7 / 16.6
D / -3.0 / -4.7
E / -15.4 / -23.9
F / -10.1 / -15.7
G / -10.7 / -16.6
H / -7.7 / -12.0
2.22. From IBC seismic design force requirements
** If you need the background for this problem, see Ch 2.12 and Ch 2.13.
a. The formulas for the base shear. Give code reference.
- V = Cs * W, where Cs is the seismic response coefficient and W is the weight of structure.
- This formula is based on Sec 9.5.5 of ASCE 7 (Read p2.51)
b. The mapped maximum considered spectral response acceleration Ss and S1 from seismic hazard maps. Cite code reference. What is the physical significance of Ss and S1.
- IBC Sec 1615 (See C.24)
- Ss is the mapped short-period (0.2 sec) spectral acceleration and S1 is the mapped 1 sec spectral acceleration. Therefore, these values imply the expected earthquake hazard for structures with short and long periods, respectively.
c. The maximum tabulated Site Class coefficients Fa and Fv. Cite Code reference. Explain the purpose of these coefficients.
** See C.42 for detail
- Fa = 2.5 for site class E and Ss≤ 0.25, and Fv = 3.5 for site class E and S1 ≤ 0.1.
- These coefficients are used to consider the effect of soil condition at your specific structure location.
d. The maximum values of SMS, SM1, SDS, and SD1, based on previous values.
** Refer to p2.53
- Using the maximum value of Ss = 3.0g,
SMS = Fa*Ss = 1.0*3.0 = 3.0g; SDS = (2/3)*SMS = (2/3)*3.0 = 2.0g
- Using the maximum value of S1 = 1.59g,
SM1 = Fv*S1 = 2.4*1.59 = 3.82g; SD1 = (2/3)*SM1 = (2/3)*3.8 = 2.55g
e. Briefly describe the purpose of the R-factor. What value of R is used for a building with wood-frame bearing walls that are sheathed with wood structural panel sheathing?
** Read p2.61
- Based on empirical evidence, it is turned out that due to reserve strength in the structural system and inelastic behavior, buildings can resist against more seismic force without collapse than what they are designed for. The R-factor can be used to reduce seismic force from the IBC design response spectrum.
- From the table on p2.63, the R-value is 6.5.
4.2 Sketch the cross section of a log. Label and define the following items:
a. Annual ring
b. The two types of wood cells
c. Heartwood and sapwood
Sol.
** Refer to Figure 4.4 on p4.12
- Annual Ring: wood cells developed on the outside of the tree in one growing season.
- Latewood: the cells which are smaller, darker, and denser
- Earlywood: the cells which are large, thinner, and lighter
- Heartwood: darker center portion of a log
- Sapwood: lighter portion of the wood near the exterior of a log
4.3 Define the following terms:
** See p4.13 and p4.14
a. Moisture content: amount of water measured as the percentage to the oven dry weight of wood
b. FSP: moisture content that corresponds to a complete loss of free water
c. EMC: average MC that lumber assumes in service
4.4 Give the moisture content range for:
** See p4.20
a. Dry lumber: MC ≤ 19%
b. Green lumber: MC > 19%
4.13 Give the range of sizes for the following size and use subcategories. In addition, indicate whether these categories are under the general classification of Dimension lumber and Timbers
(Material is Southern Pine.)
Size / Size Category / NDS Tablea / 10*12 / P & T / 4D
b / 14*14 / P & T / 4D
c / 4*8 / Dimension / 4B
d / 4*4 / Dimension / 4B
e / 2*12 / Dimension / 4B
f / 6*12 / B & S / 4D
g / 8*12 / B & S / 4D
h / 8*10 / P & T / 4D
4.16 Give the tabulated design values for No.1 DF-L for the following sizes. List values for Fb, Ft, Fv, Fc┴, Fc, and E. Give table reference.
(unit: psi)
c, d, and e(Table 4A) / f and h (Table 4D) / a, b, and g (Table 4D)
WWCLIB / WWPA / WWCLIB / WWPA
Fb / 1000 / 1350 / 1350 / 1200 / 1200
Ft / 675 / 675 / 675 / 825 / 825
Fv / 180 / 170 / 170 / 170 / 170
Fc┴ / 625 / 625 / 625 / 625 / 625
Fc / 1500 / 925 / 925 / 1000 / 1000
E / 1700000 / 1600000 / 1600000 / 1600000 / 1600000