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3. (35p) Consider a cantilever beam of length I. and circular section of radius R. The beam is loaded in pure bending by a moment M applied at the free end a) Write the value of the deflection of the free end as predicted by linear elasticity. This is given in any Strength of Materials text and available online. Consider the Young's modulus of the beam material to be E. Assume the beam is heated up to a homologous temperature...
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Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected to an increase in temperature of 60°C in an unnatural environment. The equation governing the displacement of the elastic column and the finite element stiffness matrix are respectively given as -O and ΑΕ) - where A is the cross sectional area of the beam, E is the Young's modulus of the beam material, u is the displacement and / is the finite element length....
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A cantilever beam AB with a circular cross section and length L = 750 mm supports a load P = 800 N acting at the free end (see figure). The beam is made of steel with an allowable bending stress of l20 MPa. Determine the required diameter d_min (figure part a) of the beam, considering the effect of the beam's own weight. Repeat part (a) if the beam is hollow with wall thickness t = d/8 (figure part b); compare...
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Consider a cantilever beam of length L with a fixed vertical load, Po, applied at a random distance, z, fron the fixed end of the beam. Assumeェis uniformly distributed, fx (z) = CIH (z-L/2)-H(z-L)]. (a) What is C? (b) What is the expected value of the bending moment at the root of the cantilever? (c) Suggest two possible modes in which the structure could fail to perform properly under the specified load. (d) For one of the two failure modes...
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please help both parts thx so much for help
Question 3 1) Consider Beam ACB in Figure Q3(1), determine the maximum positive moment at point C (mid-point of span AB) of the beam and show the corresponding locations of the moving loads. A moment rendering the beam bottom tension is considered positive. (14 marks) 8 kN 4 kN 6 kN 5 m Figure Q3(1) 2) Consider the cantilever shown in Figure Q3(2), draw the influence lines for (a) the moment...
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Please answer ALL questions. Neat handwriting would be great
aswell. Cheers
Question A cantilever box beam carrying a point load of 0.36 kN at its tip is to be constructed from 4 boards nailed together as shown in Fig 1. Assume that each Nail B can carry a maximum shear force of 0.13 kN. (a) Draw the SFD of the cantilever beam and determine the shear force at mid-span. (b) Draw the shear stress distribution across the section at mid-span...
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12. (5 pt.) If the circular conductor undergoes thermal expansion while it is in a uniform magnetic field, a current will be induced clockwise around it (lind). Which statement is correct? A. Bind is out of the page, so the magnetic field is directed out of the page B. Bindis out of the page, so the magnetic field is directed into the page C. Bina is into the page, so the magnetic field is directed into the page D. Bind...
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Question 1 1 pts 1. Consider a circular rod with a diameter of 2 inches and a length of 30 inches. The rod is pinned at both ends (load case a in our text book). Find the slenderness ratio. (Le/p ). Enter your answer as xx.x. Question 2 2 pts 2. Consider a hollow circular rod, with diameter of 2 inches and a wall thickness of 0.1 inch, and a length of 30 inches. The rod is pinned at both...
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SOLVE B AND C USING CASTIGLIANO'S THEOREM
Consider the cantilever beam shown in . Suppose that LAB = 640(106) mm IBC = 150(106) mm". Take E 200 GPa 12 kN/m 8 kN/m موا Inc Part A Part B Determine the displacement at point C measured downward. Use Castigliano's theorem. Express your answer to three significant figures and include the appropriate units. Enter positive value if the displacement is downward and negative value if the displacement is upward. HA ? Ac...
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(9%) Problem 4: In this problem you will consider the effect that thermal expansion due to temperature will have on Archimedes' principle. Take the densities of water and copper at O'C to be 1.00 x 10 kg/m and 8.90 x 10 kg/m", respectively. 50% Part(a) Calculate the fraction of a copper block's weight that is supported by the buoyant force at O'C. F/Wc.(0°C) = 0 Grade Summary Deductions 00 Potential 1004 ( 7 8 9 E A 4 5 6...
3. (35p) Consider a cantilever beam of length I. and circular section of radius R. The beam is loaded in pure bending by a moment M applied at the free end a) Write the value of the deflection of the free end as predicted by linear elasticity. This is given in any Strength of Materials text and available online. Consider the Young's modulus of the beam material to be E. Assume the beam is heated up to a homologous temperature...
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected to an increase in temperature of 60°C in an unnatural environment. The equation governing the displacement of the elastic column and the finite element stiffness matrix are respectively given as -O and ΑΕ) - where A is the cross sectional area of the beam, E is the Young's modulus of the beam material, u is the displacement and / is the finite element length....
A cantilever beam AB with a circular cross section and length L = 750 mm supports a load P = 800 N acting at the free end (see figure). The beam is made of steel with an allowable bending stress of l20 MPa. Determine the required diameter d_min (figure part a) of the beam, considering the effect of the beam's own weight. Repeat part (a) if the beam is hollow with wall thickness t = d/8 (figure part b); compare...
Consider a cantilever beam of length L with a fixed vertical load, Po, applied at a random distance, z, fron the fixed end of the beam. Assumeェis uniformly distributed, fx (z) = CIH (z-L/2)-H(z-L)]. (a) What is C? (b) What is the expected value of the bending moment at the root of the cantilever? (c) Suggest two possible modes in which the structure could fail to perform properly under the specified load. (d) For one of the two failure modes...
please help both parts thx so much for help
Question 3 1) Consider Beam ACB in Figure Q3(1), determine the maximum positive moment at point C (mid-point of span AB) of the beam and show the corresponding locations of the moving loads. A moment rendering the beam bottom tension is considered positive. (14 marks) 8 kN 4 kN 6 kN 5 m Figure Q3(1) 2) Consider the cantilever shown in Figure Q3(2), draw the influence lines for (a) the moment...
Please answer ALL questions. Neat handwriting would be great
aswell. Cheers
Question A cantilever box beam carrying a point load of 0.36 kN at its tip is to be constructed from 4 boards nailed together as shown in Fig 1. Assume that each Nail B can carry a maximum shear force of 0.13 kN. (a) Draw the SFD of the cantilever beam and determine the shear force at mid-span. (b) Draw the shear stress distribution across the section at mid-span...
12. (5 pt.) If the circular conductor undergoes thermal expansion while it is in a uniform magnetic field, a current will be induced clockwise around it (lind). Which statement is correct? A. Bind is out of the page, so the magnetic field is directed out of the page B. Bindis out of the page, so the magnetic field is directed into the page C. Bina is into the page, so the magnetic field is directed into the page D. Bind...
Question 1 1 pts 1. Consider a circular rod with a diameter of 2 inches and a length of 30 inches. The rod is pinned at both ends (load case a in our text book). Find the slenderness ratio. (Le/p ). Enter your answer as xx.x. Question 2 2 pts 2. Consider a hollow circular rod, with diameter of 2 inches and a wall thickness of 0.1 inch, and a length of 30 inches. The rod is pinned at both...
SOLVE B AND C USING CASTIGLIANO'S THEOREM
Consider the cantilever beam shown in . Suppose that LAB = 640(106) mm IBC = 150(106) mm". Take E 200 GPa 12 kN/m 8 kN/m موا Inc Part A Part B Determine the displacement at point C measured downward. Use Castigliano's theorem. Express your answer to three significant figures and include the appropriate units. Enter positive value if the displacement is downward and negative value if the displacement is upward. HA ? Ac...
(9%) Problem 4: In this problem you will consider the effect that thermal expansion due to temperature will have on Archimedes' principle. Take the densities of water and copper at O'C to be 1.00 x 10 kg/m and 8.90 x 10 kg/m", respectively. 50% Part(a) Calculate the fraction of a copper block's weight that is supported by the buoyant force at O'C. F/Wc.(0°C) = 0 Grade Summary Deductions 00 Potential 1004 ( 7 8 9 E A 4 5 6...