Answer:
Tmax= 46.0 lb-in
Explanation:
Given:
- The diameter of the steel rod BC d1 = 0.25 in
- The diameter of the copper rod AB and CD d2 = 1 in
- Allowable shear stress of steel τ_s = 15ksi
- Allowable shear stress of copper τ_c = 12ksi
Find:
Find the torque T_max
Solution:
- The relation of allowable shear stress is given by:
τ = 16*T / pi*d^3
T = τ*pi*d^3 / 16
- Design Torque T for Copper rod:
T_c = τ_c*pi*d_c^3 / 16
T_c = 12*1000*pi*1^3 / 16
T_c = 2356.2 lb.in
- Design Torque T for Steel rod:
T_s = τ_s*pi*d_s^3 / 16
T_s = 15*1000*pi*0.25^3 / 16
T_s = 46.02 lb.in
- The design torque must conform to the allowable shear stress for both copper and steel. The maximum allowable would be:
T = min ( 2356.2 , 46.02 )
T = 46.02 lb-in
Answer:
true
Explanation:
True, there are several types of polymers, thermoplastics, thermosets and elastomers.
Thermosets are characterized by having a reticulated structure, so they have low elasticity and cannot be stretched when heated.
Because of the above, thermosetting polymers burn when heated.
Answer:
The answer is "2 m/s".
Explanation:
The triangle from of the right angle:
![\to (x_c-0.8)+(1.5+y_4) +\sqrt{x_c^2 + 1.5^2}= constant](https://tex.z-dn.net/?f=%5Cto%20%28x_c-0.8%29%2B%281.5%2By_4%29%20%2B%5Csqrt%7Bx_c%5E2%20%2B%201.5%5E2%7D%3D%20constant)
Differentiating the above equation:
![\to V_c +V_A+ \frac{X_cV_c}{\sqrt{x_c^2 +1}}=0\\\\\to 1-V_A+ \frac{0.8 \times 1.5}{\sqrt{ 0.8^2+1.5}}=0\\\\](https://tex.z-dn.net/?f=%5Cto%20V_c%20%2BV_A%2B%20%5Cfrac%7BX_cV_c%7D%7B%5Csqrt%7Bx_c%5E2%20%2B1%7D%7D%3D0%5C%5C%5C%5C%5Cto%201-V_A%2B%20%5Cfrac%7B0.8%20%5Ctimes%201.5%7D%7B%5Csqrt%7B%200.8%5E2%2B1.5%7D%7D%3D0%5C%5C%5C%5C)
![\to V_A= \frac{1.2}{\sqrt{ 0.64+1.5}}+1\\\\](https://tex.z-dn.net/?f=%5Cto%20V_A%3D%20%20%5Cfrac%7B1.2%7D%7B%5Csqrt%7B%200.64%2B1.5%7D%7D%2B1%5C%5C%5C%5C)
![= \frac{1.2}{ 1.46}+1\\\\= \frac{1.2+ 1.46}{ 1.46}\\\\ = \frac{2.66}{1.46}\\\\= 1.82 \ \frac{m}{s}\\\\= 2 \ \frac{m}{s}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1.2%7D%7B%201.46%7D%2B1%5C%5C%5C%5C%3D%20%5Cfrac%7B1.2%2B%201.46%7D%7B%201.46%7D%5C%5C%5C%5C%20%3D%20%5Cfrac%7B2.66%7D%7B1.46%7D%5C%5C%5C%5C%3D%201.82%20%5C%20%5Cfrac%7Bm%7D%7Bs%7D%5C%5C%5C%5C%3D%202%20%5C%20%5Cfrac%7Bm%7D%7Bs%7D)
Answer:
The value of Modulus of elasticity E = 85.33 ×
![\frac{lbm}{in^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Blbm%7D%7Bin%5E%7B2%7D%20%7D)
Beam deflection is = 0.15 in
Explanation:
Given data
width = 5 in
Length = 60 in
Mass of the person = 125 lb
Load = 125 × 32 = 4000![\frac{ft lbm}{s^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Bft%20lbm%7D%7Bs%5E%7B2%7D%20%7D)
We know that moment of inertia is given as
![I = \frac{bt^{3} }{12}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7Bbt%5E%7B3%7D%20%7D%7B12%7D)
![I = \frac{5 (1.5^{3} )}{12}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B5%20%281.5%5E%7B3%7D%20%29%7D%7B12%7D)
I = 1.40625 ![in^{4}](https://tex.z-dn.net/?f=in%5E%7B4%7D)
Deflection = 0.15 in
We know that deflection of the beam in this case is given as
Δ = ![\frac{PL^{3} }{48EI}](https://tex.z-dn.net/?f=%5Cfrac%7BPL%5E%7B3%7D%20%7D%7B48EI%7D)
![0.15 = \frac{4000(60)^{3} }{48 E (1.40625)}](https://tex.z-dn.net/?f=0.15%20%3D%20%5Cfrac%7B4000%2860%29%5E%7B3%7D%20%7D%7B48%20E%20%281.40625%29%7D)
E = 85.33 ×
![\frac{lbm}{in^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Blbm%7D%7Bin%5E%7B2%7D%20%7D)
This is the value of Modulus of elasticity.
Beam deflection is = 0.15 in