A three-phase, 318.75kVA, 2300-Volt, alternator has an armature resistance of 0.35/phase and a synchronous reactance of 1.2/phas
e. Determine the no-load lineto- line generated voltage and the voltage regulation at:
1 answer:
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Answer:
the rate of flow of heat through the roof is 45616.858 BTU/hr
Explanation:
Given the data in the question;
pin thickness = 2 in
fiber glass thickness = 4 in
Asphalt shingles thickness = 0.1 in
R/inch for pine = 1.28
R/inch for fiberglass = 3.0
R/inch for Shingles = 4.0
Temperature inside the house = 700 F
Temperature outside the house = 300 F
area of the roof A = 500 ft²
we calculate the total Resistance;
R = ( 2 × 1.28 ) + ( 4 × 3.0 ) + ( 0.1 × 4.0 )
R = 2.56 + 12 + 0.4
R = 14.96
Now, we determine the rate of heat flow;
dQ/dt = ΔT(A) / R
⇒ ( -
)A / R
we substitute
⇒ (( 700 - 300 ) × 500 ) / 14.96
⇒ ( 400 × 500 ) / 14.96
⇒ 200000 / 14.96
⇒ 13368.98 watt
we know that 1 watt = 3.412142 BTU/hr
⇒ ( 13368.98 × 3.412142 ) BTU/hr
⇒ 45616.858 BTU/hr
Therefore, the rate of flow of heat through the roof is 45616.858 BTU/hr
Answer: ASD = 306 kips-ft
LRSD = 1387.5 k-ft
Explanation:
To begin, we will take a step by step process to solving this problem.
Attached below is a picture to guide us to solving this.
To begin, we have that to reaction of the support
ΣMд = 0
where;
RB * 35 - (8+18)15 - (4+9)20 = 0
RB = 18.57k
also Ey = 0;
RA + RB = 18 + 8 + 9 +4 = 20.43 k
taking the maximum moment at mid point;
Mc = RA * 35/2 - (8 +18) (35/2 -15)
Mc = 292.525
therefore, MD = RA * 15 = 20.43 * 15 = 306.45 k.ft
MD = 306.45 k.ft
ME = 279 k.ft i.e 18.57 * 15
considering the unsupported length; 35 - (15*2 = 5ft
now we have that;
Lb = Lp = 5ft
where Lp = 1.76 ry(√e/fy)
Lp = 1.76 ry √29000/50 ......
ry = 1.4 inch
so we have that Mr = Mp for Lb = Lp where
Mp = 2 Fy ≤ 1.5 sx Fy
Recall from the expression,
RA + RB = (8+4) * 1.2 + (18+9) * 1.6 = 57.6
RA * 35 = 4 * 1.2 * 15 + 9 *1.6 * 15 + 8 * 1.2 * 20 + 18 * 1.6 * 20
RA = 30.17 k
the maximum moment at D = 30.17 * 15 = 452.55 k.ft
Zrequired = MD/Fy = 452.55 * 12 / 50 = 108.61 inch³
so we have Sx = 452.55 * 12 / 1.5 * 50 = 72.4 inch³
also r = 1.41 in
Taking LRFD solution:
where the design strength ∅Mn = 0.9 * Zx * Fy
given r = 2.97
Zx = 370 and Sx = 81.5, we have
∅Mn = 0.9 * 370 * 50 = 16650 k-inch = 1387.5 k-ft
this tells us it is safe.
ASD solution:
for Lb = Lp, and where Mn = Mp = Fcr Sx
we already have value for Sx as 81.5 so
Fcr = ZxFy/Sx
Fcr = 370 * 50 / 81.5 = 227 ksi
considering the strength;
Strength = Mn / Ωb = (0.6 * 81.5 * 50) * (1.5) / 12 = 306 kips-ft
This justifies that it is safe because is less than 306
cheers i hope this helps.
