energy moment
The arrangement of a street light post is given below. The cross-section of allthe bars are circular. The diameter of the lower section of the post is 1.5 times of other parts of the post. a. State the expression for the bending moment and the energy due to bending moment of the section BCb. State the expression for the bending moment and the energy due to bending moment of the section AB.c. Hence calculate the vertical deflection at C. A is the cross-sectional area and E is the Young’s Modulus. 
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Using the theorem of Castigliano, find the vertical and horizontal deflection of the free end at...
Using the theorem of Castigliano, find the vertical and horizontal deflection of the free end at point d due to the horizontal applied load F for the cantilever frame shown in the figure. Express your answers in terms of F, I, I, E (modulus of elasticity), A cross sectional area) and I (moment of inertia of the cross section around the bending axis.). Consider only bending and axial loading, and assume that the cross sectional is circular. be ay
A beam may have zero shear stress at a section but may not have zero deflection;...
A beam may have zero shear stress at a section but may not have zero deflection; Hence, bending is primarily caused by bending moment In Torsion loading a stress element in a circular rod is subject to shear state The principal plane and the plane on which the shear stresses are maximum, they make 90 degree angle between them. If the Torque on a steel circular shaft (G=80 GPa) is 13.3 kN-m and the allowable shear stress is 98 MPa,...
6. If the stresses and strains at a point in a linear elastic material are given...
6. If the stresses and strains at a point in a linear elastic
material are given by
σij = ε
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
=
885 154 0
154 1038 615
0 615 577
0 002 0 001 0
0 001 0 003 0 004
0 0 004 0
MPa; and ij
. .
. . .
.
respectively, determine (i) the total strain energy density in the
material, (ii) the hydrostatic...
u Review Part B - Calculate the moment of inertia Learning Goal: To find the centroid...
u Review Part B - Calculate the moment of inertia Learning Goal: To find the centroid and moment of inertia of an I-beam's cross section, and to use the flexure formula to find the stress at a point on the cross section due to an internal bending moment. Once the position of the centroid is known, the moment of inertia can be calculated. What is the moment of inertia of the section for bending around the z-axis? Express your answer...
03(a) A reinforced concrete beam is acted on by a positive bending moment. reinforcement consists of 4 bars of 28 mm diameter. The modulus of elasticity is E 25 GPa for the concrete and E-200 G...
03(a) A reinforced concrete beam is acted on by a positive bending moment. reinforcement consists of 4 bars of 28 mm diameter. The modulus of elasticity is E 25 GPa for the concrete and E-200 GPa for the steel. The allowable stresses for the concrete and steel are ơ.-9.2 MPa and ơ.-135 MPa, respectively. Determine the maximum permissible positive bending moment. (10 marks) 625 mm 4 bars 28 mm -300 mm Figure Q3(a) 03(b) A simply supported beam that is...
The rigid beam ACE is subjected to the load P and suspended at points A, C, and E
The rigid beam ACE is subjected to the load P and suspended at points A, C, and E by three suspender bars AB, CD, and EF (see Figure 1). These three suspender bars are made of the same steel and have the same circular cross section with the same diameter of d=30 mm. The ultimate 2m stress of steel is σu=450 MPa and Young modulus is E=200 GPa. (a) Using a factor of safety FS=1.5, determine the All maximum allowable load...
Part A - Moment about the x axis at A Learning Goal: To determine the state...
Part A - Moment about the x axis at A Learning Goal: To determine the state of stress in a solid rod using the principle of superposition. A solid rod has a diameter of e = 60 mm and is subjected to the loading shown. Let a = 200 mm, b = 220 mm c = 340 mm, d = 230 mm, and P = 4.0 kN. Take point A to be at the top of the circular cross-section. (Figure...
3. Power transmission is an important engineering application and relies on the integrity of the shaft designs. Assume a solid, circular steel shaft with a uniform diameter d 50 mm and a total le...
3. Power transmission is an important engineering application and relies on the integrity of the shaft designs. Assume a solid, circular steel shaft with a uniform diameter d 50 mm and a total length I3 m. At its midpoint, a belt passes over a pulley and delivers 50 kW power to the shaft. This power is used to drive two machines at either end of the shaft. Machine 1 consumes P1 20 kW and machine 2 uses P230 KW. The...
please help with steps to solve this problem Figure 2 [25] QUESTION 3 A pinned-pinned round...
please help with steps to solve this problem
Figure 2 [25] QUESTION 3 A pinned-pinned round bar is to be 4m long. It is subjected to a purely axial load. Determine the diameter of the bar and determine the maximum load that it can carry if the bar is made of steel with yield strength of 280 MPa and an elastic modulus of 207 GPa. The safety factor on yield should not exceed 1.5. The moment of inertia for a...
Problem 4 Member A is a steel rod with circular cross-section. The modulus of elasticity is...
Problem 4 Member A is a steel rod with circular cross-section. The modulus of elasticity is 29000 ksi. Member B is very stiff compared to Member A, so ignore its deformations. a. Set up the virtual force system for vertical displacements DEAD 20K LIVE 10 k at Node 2. Determine the minimum diameter of rod that can be used if the deflection due to live load cannot exceed 0.5 in Assume that rods are available in 1/8 in. increments, such...
Using the theorem of Castigliano, find the vertical and horizontal deflection of the free end at point d due to the horizontal applied load F for the cantilever frame shown in the figure. Express your answers in terms of F, I, I, E (modulus of elasticity), A cross sectional area) and I (moment of inertia of the cross section around the bending axis.). Consider only bending and axial loading, and assume that the cross sectional is circular. be ay
A beam may have zero shear stress at a section but may not have zero deflection; Hence, bending is primarily caused by bending moment In Torsion loading a stress element in a circular rod is subject to shear state The principal plane and the plane on which the shear stresses are maximum, they make 90 degree angle between them. If the Torque on a steel circular shaft (G=80 GPa) is 13.3 kN-m and the allowable shear stress is 98 MPa,...
6. If the stresses and strains at a point in a linear elastic
material are given by
σij = ε
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
=
885 154 0
154 1038 615
0 615 577
0 002 0 001 0
0 001 0 003 0 004
0 0 004 0
MPa; and ij
. .
. . .
.
respectively, determine (i) the total strain energy density in the
material, (ii) the hydrostatic...
u Review Part B - Calculate the moment of inertia Learning Goal: To find the centroid and moment of inertia of an I-beam's cross section, and to use the flexure formula to find the stress at a point on the cross section due to an internal bending moment. Once the position of the centroid is known, the moment of inertia can be calculated. What is the moment of inertia of the section for bending around the z-axis? Express your answer...
03(a) A reinforced concrete beam is acted on by a positive bending moment. reinforcement consists of 4 bars of 28 mm diameter. The modulus of elasticity is E 25 GPa for the concrete and E-200 GPa for the steel. The allowable stresses for the concrete and steel are ơ.-9.2 MPa and ơ.-135 MPa, respectively. Determine the maximum permissible positive bending moment. (10 marks) 625 mm 4 bars 28 mm -300 mm Figure Q3(a) 03(b) A simply supported beam that is...
Part A - Moment about the x axis at A Learning Goal: To determine the state of stress in a solid rod using the principle of superposition. A solid rod has a diameter of e = 60 mm and is subjected to the loading shown. Let a = 200 mm, b = 220 mm c = 340 mm, d = 230 mm, and P = 4.0 kN. Take point A to be at the top of the circular cross-section. (Figure...
3. Power transmission is an important engineering application and relies on the integrity of the shaft designs. Assume a solid, circular steel shaft with a uniform diameter d 50 mm and a total length I3 m. At its midpoint, a belt passes over a pulley and delivers 50 kW power to the shaft. This power is used to drive two machines at either end of the shaft. Machine 1 consumes P1 20 kW and machine 2 uses P230 KW. The...
please help with steps to solve this problem
Figure 2 [25] QUESTION 3 A pinned-pinned round bar is to be 4m long. It is subjected to a purely axial load. Determine the diameter of the bar and determine the maximum load that it can carry if the bar is made of steel with yield strength of 280 MPa and an elastic modulus of 207 GPa. The safety factor on yield should not exceed 1.5. The moment of inertia for a...
Problem 4 Member A is a steel rod with circular cross-section. The modulus of elasticity is 29000 ksi. Member B is very stiff compared to Member A, so ignore its deformations. a. Set up the virtual force system for vertical displacements DEAD 20K LIVE 10 k at Node 2. Determine the minimum diameter of rod that can be used if the deflection due to live load cannot exceed 0.5 in Assume that rods are available in 1/8 in. increments, such...
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