Answer:
W = 2695.14 lb
Explanation:
given,
side of cube = 3 ft
density of the cube = 3.1 slugs/ft³
we know,
mass = density x volume
volume = 3³ = 27 ft³
mass = 3.1 x 27
m = 83.7 slugs.
weight calculation
converting mass from slug to pound
weight of 1 slug is equal to 32.2 lb
now,
weight of the cube is equal to
W = 83.7 slugs x 32.2 lb/slug
W = 2695.14 lb
hence, weight is equal to W = 2695.14 lb
Explanation:
Specific cutting energy:
It the ratio of power required to cut the material to metal removal rate of material.If we take the force required to cut the material is F and velocity of cutting tool is V then cutting power will be the product of force and the cutting tool velocity.
Power P = F x V
Lets take the metal removal rate =MRR
Then the specific energy will be
If we consider that metal removal rate and cutting tool velocity is constant then when we increases the cutting force then specific energy will also increase.
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.
