Homework Answers
The compatibility equation:
the total deformation of the member is zero since it is fixed at both the ends.
Therefore, delta =0
delta(AB) + delta (BC) = 0
Therefore, second option is correct.
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RB (a) FIG. 2-16 Analysis of a statically indeterminate bar What is the compatibility equation that...
KHW 9: force method Force Method of Analysis: Frames 2 of 5> statically indeterminate. Choosing S...
KHW 9: force method Force Method of Analysis: Frames 2 of 5> statically indeterminate. Choosing S and Cy as the redundant forces leads to the superposition shown. The flexibility coefficient Bo relates the deflection at point B to the redundant force at C The compatibility equations are written by requiring the displacements at the redundant locations to be consistent between the real beam and the model formed by the superposition of the statically determinate beams. Part A -Deflection of th...
no need for ms solids 3 Statically indeterminate end-to-end bars. Given: The two-bar structure is fixed...
no need for ms solids
3 Statically indeterminate end-to-end bars. Given: The two-bar structure is fixed at both ends and a 0.01 in. gap exists between the two bars, as shown in Figure 3. Bar l is made of Aluminum 2014-T6, the elastic modulus isEal umum. 6 ksi, the linear coefficient of thermal expansions is αalun in 12.8(10 6) F, and cross-section area of Bar l is Al-05 in. Bars 2 is made of Steel-A36 Structural with Estss 29000 ksi,...
To solve for forces in statically indeterminate bars with axial loads.
To solve for forces in statically indeterminate bars with axial loads.When the number of reaction forces is greater than the number of equilibrium equations, the system is statically indeterminate. Solving for the reactions requires some additional equations. These additional equations come from considering compatibility relationships (i.e.) continuity of displacements and relationships between displacements and loads).For an axially loaded member, the compatibility relationship for the deflections can be written by setting the total relative axial displacement between the ends of the...
Learning Goal: To solve for forces in statically indeterminate bars with axial loads. Consider a new...
Learning Goal: To solve for forces in statically indeterminate bars with axial loads. Consider a new structure, where the thickness of the bar is reduced to 32.5 mm from C to B (it is still square) (Figure 2) and <= 3.75 m. If the applied load is F - 370 kN , then what is the reaction at ? Let a positive reaction act to the right. The total length is still 6 m Express your answer with appropriate units...
please use moment equation too. It is statically indeterminate, more data is not required. need to...
please use moment equation too. It is statically indeterminate,
more data is not required. need to use moment equations.
2. The beam shown is made of aluminum 6061-T6 and has cross-sectional moment of inertia of 250 in?. Determine the reactions at the supports and the maximum deflection. 600 lb/ft 10 Kip ft2 kip B 3 ft 6 ft - - 8ft -
Learning Goal: To solve for forces in statically indeterminate bars with axial loads. Part A-Force with...
Learning Goal: To solve for forces in statically indeterminate bars with axial loads. Part A-Force with a known deflection When the number of reaction forces is greater than the number of equilibrium equations, the system is statically indeterminate. Solving for the reactions requires some additional equations. These additional equations come from considering compatibility relationships (i.e., continuity of displacements and relationships between displacements and loads). The square bar shown (Figure 1) is 72.5 mm thick and 3.6 m long and is...
2) Consider a statically indeterminate beam in (I) = (i) + (ii) + (iii) as shown. a) Using your cheat sheet, compute the solutions of (i), (ii) and (iii) (A to B) respectively in terms of w0, P...
2) Consider a statically indeterminate beam in
(I) = (i) + (ii) + (iii) as shown.
a) Using your cheat
sheet, compute the solutions of (i), (ii)
and (iii) (A to B) respectively
in terms of w0, P and
Q.
b) Compute for (i), (ii) and (iii) at the free end B.
b) Impose the constraint at B to solve
for the reaction
Q=RB
(<0) at B.
c) Find the elastic curve of
(I), the (+2)force & moment
reactions at...
Q2. Statically determinate or indeterminate truss analysis by the stiffness method. (50 marks) a) Determine the stiffness matrix of the whole truss given in problems 14.9 and 14.10 (p. 583). Indicate...
Q2. Statically determinate or indeterminate truss analysis by
the stiffness method. (50 marks)
a) Determine the stiffness matrix of the whole truss given in
problems 14.9 and 14.10 (p. 583). Indicate the degrees-of freedom
in all the stiffness matrices. (18 marks)
b) Calculate all the nodal displacements and all the member forces
for the truss.
(16 marks)
14-9. Determine the stiffness matrix K for the trus Take A 0.0015 m2 and E 200 GPa for each member. 2 12 4...
What is the reaction Ax to the nearest 0.01 kN for the following frame? El are...
What is the reaction Ax to the nearest 0.01 kN for the following frame? El are constant and the same for all members. Consider only bending energy. W = 67 kN/m w -5 m-+ 10 m ---5 m 5 m А B 422 CHAPTER 10 ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES BY THE FORCE METHOD 10.5 Force Method of Analysis: Frames The force method is very useful for solving problems involving statically indeterminate frames that have a single story and unusual...
EXAMPLE 16.5 The large window in Fig. 16-10 is opened using a hydraulic cylinder AB. If...
EXAMPLE 16.5 The large window in Fig. 16-10 is opened using a hydraulic cylinder AB. If the cylinder extends at a constant rate of 0.5 m/s, determine the angular velocity and angular acceleration of the window at the instant 0 30° 1 m SOLUTION Position Coordinate Equation. The angular motion of the window can be obtained using the coordinate 0, whereas the extension or motion along the hydraulic cylinder is defined using a coordinate s, which measures its length from...
KHW 9: force method Force Method of Analysis: Frames 2 of 5> statically indeterminate. Choosing S and Cy as the redundant forces leads to the superposition shown. The flexibility coefficient Bo relates the deflection at point B to the redundant force at C The compatibility equations are written by requiring the displacements at the redundant locations to be consistent between the real beam and the model formed by the superposition of the statically determinate beams. Part A -Deflection of th...
no need for ms solids
3 Statically indeterminate end-to-end bars. Given: The two-bar structure is fixed at both ends and a 0.01 in. gap exists between the two bars, as shown in Figure 3. Bar l is made of Aluminum 2014-T6, the elastic modulus isEal umum. 6 ksi, the linear coefficient of thermal expansions is αalun in 12.8(10 6) F, and cross-section area of Bar l is Al-05 in. Bars 2 is made of Steel-A36 Structural with Estss 29000 ksi,...
Learning Goal: To solve for forces in statically indeterminate bars with axial loads. Consider a new structure, where the thickness of the bar is reduced to 32.5 mm from C to B (it is still square) (Figure 2) and <= 3.75 m. If the applied load is F - 370 kN , then what is the reaction at ? Let a positive reaction act to the right. The total length is still 6 m Express your answer with appropriate units...
please use moment equation too. It is statically indeterminate,
more data is not required. need to use moment equations.
2. The beam shown is made of aluminum 6061-T6 and has cross-sectional moment of inertia of 250 in?. Determine the reactions at the supports and the maximum deflection. 600 lb/ft 10 Kip ft2 kip B 3 ft 6 ft - - 8ft -
Learning Goal: To solve for forces in statically indeterminate bars with axial loads. Part A-Force with a known deflection When the number of reaction forces is greater than the number of equilibrium equations, the system is statically indeterminate. Solving for the reactions requires some additional equations. These additional equations come from considering compatibility relationships (i.e., continuity of displacements and relationships between displacements and loads). The square bar shown (Figure 1) is 72.5 mm thick and 3.6 m long and is...
2) Consider a statically indeterminate beam in
(I) = (i) + (ii) + (iii) as shown.
a) Using your cheat
sheet, compute the solutions of (i), (ii)
and (iii) (A to B) respectively
in terms of w0, P and
Q.
b) Compute for (i), (ii) and (iii) at the free end B.
b) Impose the constraint at B to solve
for the reaction
Q=RB
(<0) at B.
c) Find the elastic curve of
(I), the (+2)force & moment
reactions at...
Q2. Statically determinate or indeterminate truss analysis by
the stiffness method. (50 marks)
a) Determine the stiffness matrix of the whole truss given in
problems 14.9 and 14.10 (p. 583). Indicate the degrees-of freedom
in all the stiffness matrices. (18 marks)
b) Calculate all the nodal displacements and all the member forces
for the truss.
(16 marks)
14-9. Determine the stiffness matrix K for the trus Take A 0.0015 m2 and E 200 GPa for each member. 2 12 4...
What is the reaction Ax to the nearest 0.01 kN for the following frame? El are constant and the same for all members. Consider only bending energy. W = 67 kN/m w -5 m-+ 10 m ---5 m 5 m А B 422 CHAPTER 10 ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES BY THE FORCE METHOD 10.5 Force Method of Analysis: Frames The force method is very useful for solving problems involving statically indeterminate frames that have a single story and unusual...
EXAMPLE 16.5 The large window in Fig. 16-10 is opened using a hydraulic cylinder AB. If the cylinder extends at a constant rate of 0.5 m/s, determine the angular velocity and angular acceleration of the window at the instant 0 30° 1 m SOLUTION Position Coordinate Equation. The angular motion of the window can be obtained using the coordinate 0, whereas the extension or motion along the hydraulic cylinder is defined using a coordinate s, which measures its length from...
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