SUSTAINABLE ENERGY (LL)
2nd Edition
ISBN: 9780357667224
Author: DUNLAP
Publisher: CENGAGE L
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Chapter 8, Problem 8P
Compare the masses and volumes of water, concrete, sand, and wood needed to store 106 Btu of heat if the operating temperatures are Tc = 85°F and Th = 180°F. In each case, calculate the edge length of a square storage unit with a height of 8 ft.
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SITUATION 2: An 8-meter simply supported beam is to be loaded, in addition to its self-weight, a triangular
distributed load that linearly increases from zero at the left support to 20 kN/m (dead) + 35 kN/m (live) at the
right support. It is braced laterally at the end supports and at midspan. The details for the beam cross-section
are given below. Use the LRFD provisions of NSCP 2015.
W 540 mm x 150 kg/m:
Area, A 19,225 mm²
Depth, D = 540 mm
Clear Distance between Flanges, h = 455 mm
Flange width, bf=310 mm
Flange thickness, tf = 20 mm
Web thickness, tw 12.5 mm
Elastic Section Modulus, Sx = 3.72 x 106 mm³
Plastic Section Modulus, Zx = 4.14 x 10 mm³
Torsional Constant, J = 2.04 x 10% mm*
Distance between flange centroids, ho = 520 mm
Radius of gyration along y-axis, ry = 72 mm
Cb = 1.196
Effective radius of gyration, rts = 85 mm
Yield Strength of Steel, Fy = 345 MPa
Modulus of Elasticity, E=200 GPa
1. What is the ultimate moment capacity of the beam, in kN-m?
1. 1285.470 kN-m
SITUATION 4: A steel column W 300 x 203 kg/m is subjected to an axial load of 2670 kN. Unbraced length of
column is 3m, and assume that the column is pinned at both ends, side sway prevented. Show your complete
solution and box only the final answer.
Properties of Column:
Area, A = 25,740 mm²
Depth, d=340 mm
Flange thickness, tf = 32 mm
Flange Width, bf=315 mm
Web thickness, tw = 20 mm
Ix = 5.16 x 10 mm²
ly = 1.65 x 10° mm*
Fy = 345.6 MPa
1. Determine the design strength (kN) of the column.
2. Determine the allowable strength (kN) of the column.
3. What is the value of the slenderness ratio to be used for the column?
1. 7223.401 kN
2. 4805.988 kN
3. 37.470
Give me a steel member design problems under combined axial and bending forces, using interaction equations, with complete solution and final answer
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- (a) Determine the Nataf model for the joint PDF fxx, (xx) of the basic (physical) random variables X₁ and X, with marginal PDF's fx(x)=e, 0≤x (Exponential distribution) fx₁ (x2)=x2e-0.5x, 0≤x (Rayleigh distribution) and correlation coefficient Pxx=0.50 Note: Use Table 6 of paper by Liu and Der Kiureghian, 1986. (b) Generate a 3D surface plot and contour plot of the joint PDF fxx, (x,x) using Matlab or any other software of your choice. (c) What is the standard deviation of X2? (d) Construct a transformation from the physical X space (defined by random variables X, and X,) to the standard normal U space (defined by the statistically independent standard normal random variables (U, and U₂), i.e., U=T(X). Also describe the inverse transform X=T(U) and the Jacobian matrices J = ди θα and Ju Ox ди (e) According to the inverse transformation X = T¹ (U) and using Matlab, generate 1,000 samples from the Nataf joint PDF fxx, (x1,x2) derived in part (a). Start by generating samples of U using a…arrow_forwardBased on the results obtained, comment on the relative importance of the body and the tails of thedistributions of R and S on the probability of failure with increasing central safety factor CSF .arrow_forward1. The beam is supported by a roller constraint at B, which allows vertical displacement but resists axial load and moment. If the bar is subjected to the loading shown and constant El (L = 12 ft, E = 3100 ksi, I = 1728 in (rectangular section 12"x12"), w = 1 klf). Caution: pay attention to unit conversion between ft and in) x W B a. Sketch the deflected shape. L b. Determine the equations of the slope and the elastic curve using the coordinate x. First, solve this problem parametrically, and then substitute the numerical values for L, E, I, w at the end. There will be a significant penalty for solutions that do not calculate the slope and deflection as parametric functions. c. Specify the slope (in radians) at point A (parametrically and numerically). d. Specify the vertical displacement at point B (parametrically and numerically).arrow_forward
- 4. EI is constant in the beam below (a = 12 ft, b = 5 ft, E = 29,000 ksi, I = 800 in¹ (W18x50), P = 2 kip): b Р C a. Sketch the deflected shape. b. Determine the equations of the slope and the elastic curve using the coordinates x1 and x2. c. For the AB segment, determine the maximum deflection and its location. Hint: at maximum deflection, the slope is zero. d. Specify the slope (in radians) and deflection at point C.arrow_forward3. EI is constant in the beam below (a = 10 ft, b = 5 ft, E = 29,000 ksi, I = 340 in (W14x34), Mo = 50 k. ft): Mo Mo a. Sketch the deflected shape. X2 b. Determine the equations of the slope and the elastic curve using the coordinates x1 and x2. Due to symmetry, only the left side is sufficient. Hint: symmetry requires the slope to be zero at mid span. c. Determine the maximum deflection. d. Specify the slope (in radians) at point A.arrow_forward2. EI is constant in the beam below (L = 10 ft, E = 29,000 ksi, I = 350 in (W12x45), W = 500 lb/ft): a. Sketch the deflected shape. b. Determine the equations of the slope and the elastic curve using the coordinates x1 and X2. c. Specify the slope (in radians) and deflection at point C. d. Specify the slope (in radians) at point B. -x- L 2 W C X27 L 22 Barrow_forward
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