QUESTION BANK ENGINEERS ACADEMY. Hinge E F A D. Theory of Structures Determinacy Indeterminacy 1

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1 Theory of Structures eterminacy Indeterminacy 1 QUSTION NK 1. The static indeterminacy of the structure shown below (a) (b) 6 (c) 9 (d) etermine the degree of freedom of the following frame (a) 1 (b) 24 (c) 27 (d) 18. The force in the member of the truss in fig is 2 a a (a) statically indeterminate but unstable (b) unstable (c) determinate and stable (d) none of the above 5. etermine static and kinematic indeterminacies for trusses (a) 1, 21 (b) 2, 20 (c) 1, 22 (d) 2, The static Indeterminacy of the structure shown below is. H K (a) 4 (b) 6 I (c) 8 (d) The structure shown below is J a (a) Zero (c) (ompression) # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , (b) 2 (ompression) (d) (Tensile) 4. The plane frame shown below is : (a) externally indeterminate (b) internally indeterminate (c) determinate (d) mechanism mail : engineersacademy.org

2 2 eterminacy Indeterminacy ivil ngineering 8. The static Indeterminacy of the structure shown below is (a) unstable hinge (b) stable, determinate (c) stable, indeterminate to 5 th degree (d) stable, indeterminate to rd degree 9. etermine the degrees of freedom of the following frame. (a) 10 (b) 11 (c) 12 (d) The plane structure shown below is # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , (a) stable and determinate (b) stable and indeterminate (c) unstable and indeterminate (d) unstable and determinate 11. plane frame H shown in figure below has clamp supports at and axial force release (horizontal sleeve) at and moment release (hinge) at. The static indeterminacy of the frame is. H (a) 4 (b) (c) 2 (d) The plane figure shown below is (a) Stable and statically determinate (b) unstable and statically determinate (c) stable and statically indeterminate (d) unstable and statically indeterminate 1. The degrees of freedom of the following frames is. (a) (b) 4 (c) 5 (d) The kinematic indeterminacy of single bay portal frame fixed at the base is. (a) One (c) Three (b) Two (d) Zero 15. The kinematic indeterminacy of plane frame shown below is. (a) 1 (b) 2 (c) (d) zero mail : engineersacademy.org

3 Theory of Structures eterminacy Indeterminacy 16. beam fixed at the ends and subjected to lateral loads only is statically indeterminate and the degree of indeterminacy is 20. The following two statements are made with reference to the planar truss shown below: (a) One (c) Three (b) Two (d) our 17. The forces in members a, b and c in the truss shown I H (a),, 0 2 (c),, a (b) (d) c b,, 0 2,, The degree of kinematic indeterminacy of the rigid frame with clamped ends at and shown in the figure is I. The truss is statically determinate II. The truss is kinematically determinate. With reference to the above statements, which of the following applies? (a) oth statements are true (b) oth statements are false (c) II is true but I false (d) I is true but II is false 21. The total degree of indeterminacy (both internal and external) for the bridge truss shown in the given figure is (a) 4 (b) (c) 2 (d) Zero 19. The force in the member of the truss shown in the figure is 100kN (a) 4 (b) 5 (c) 6 (d) 22. What is the degree of static indeterminacy of the plane structure as shown in the figure below? (a) kn (c) 5.5 kn (b) zero (d) 25.0 kn (a) (b) 4 (c) 5 (d) 6 # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , mail : engineersacademy.org

4 4 eterminacy Indeterminacy ivil ngineering 2. What is the total degree of indeterminacy (both internal and external) of the triangular planar truss shown in the figure below? 26. The degree of static indeterminacy of the pinjointed plane frame shown in figure is W 2 W 1 (a) 2 (b) 4 (c) 5 (d) What is the degree of indeterminacy (both internal and external) of the cantilever plane truss shown in the figure below? W W 4 (a) 1 (b) 2 (c) (d) The frame shown below is redundant to 10 kn 5 kn 5 kn L (a) 2 (b) (c) 4 (d) onsider the following statements with respect to the figure below of a typical articulated frame : 1. The frame is internally determinate and externally indeterminate. 2. The frame is internally indeterminate and externally determinate.. The frame is internally as well as externally determinate. 4. The frame is internally as well as externally indeterminate. Which of these statements is/are correct? (a) 1 only (b) 1 and 2 (c) only (d) and 4 # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , (a) single degree (c) three degree 2L (b) two degree (d) four degree 28. Match List-I (Type of structure) with List-II (Statical indeterminacy) and select the correct answer using the codes given below the lists Number of member = m Number of joints = n Number of external reaction elements = r List-I () lane frame () Space truss () Space frame odes : (a) 1 2 (b) 4 2 (c) 2 1 (d) List-II 1. m + r n 2. 6m + r 6n. 6m + r n 4. m + r n mail : engineersacademy.org

5 Theory of Structures eterminacy Indeterminacy Total degree of indeterminacy (both internal and external) of the plane frame shown in the given figure is 4. What is the total degree of indeterminacy both internal and external of the plane frame shown below? (a) 10 (b) 11 (c) 12 (d) The degree of indeterminacy of the beam given below is (a) zero (b) one (c) two (d) three 1. onsider the following statements : 1. n indeterminate structure is not economical from material stand point in comparison to a determinate structure. 2. If n redundant in a statically indeterminate structure of n degree indeterminacy are removed the structure will become statically determinate but unstable.. In the rigid frame analysis, the axial effects are ignored as influence is negligibly small compared to bending and shear effects. Which of these statement is /are correct? (a) 1 only (b) 1 and 2 (c) only (d) 2 and 2. Which one of the following is true example of a statically determinate beam? (a) One end is fixed and the other end is simply supported (b) oth the ends are fixed (c) The beam overhangs over two supports (d) The beam is supported on three supports. The number of unknowns to be determined in the stiffness method is equal to (a) the static indeterminacy (b) the kinematic indeterminacy (c) the sum of kinematic indeterminacy and static indeterminacy (d) two times the number of supports # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , (a) 10 (b) 11 (c) 12 (d) Which one of the following structures is statically determinate and stable? (a) (c) (b) (d) 6. prismatic beam is shown in the figure given below. onsider the following statements : 1. The structure is unstable. 2. The bending moment is zero at supports and internal hinge.. It is a mechanism. 4. It is statically indeterminate. Which of these statements are correct? (a) 1, 2, and 4 (b) 1, 2 and (c) 1 and 2 (d) and 4 mail : engineersacademy.org

6 6 eterminacy Indeterminacy ivil ngineering 7. What is the degree of indeterminacy of the frame shown in the figure given below? 42. What is the number of independent degrees of freedom of the two-span continuous beam of uniform section shown in the figure below? (a) 4 (b) (c) 2 8. determinate structure (d) zero (a) cannot be analyzed without the correct knowledge of modulus of elasticity (b) must necessarily have roller support at one of its ends (c) requires only statical equilibrium equations for its analysis (d) will have zero deflection at its ends 9. statically indeterminate structure is the one which (a) cannot be analyzed at all (b) can be analyzed using equations of statics only (c) can be analyzed using equations of statics and compatibility equations (d) can be analyzed using equations of compatibility only 40. What is the statical indeterminacy for the frame shown below? (a) 1 (b) 2 (c) (d) 4 4. What is the kinematic indeterminacy for the shown below? (members are inextensible) Roller (a) 6 (b) 11 (c) 12 (d) If the axial deformation is neglected, what is the kinematic indeterminacy of a single bay portal frame fixed at base? (a) 2 (b) (c) 4 (d) or the plane frame with an overhang as shown below, assuming negligible axial deformation the degree of static indeterminacy d and the degree of kinematic indeterminacy k are (a) 12 (b) 15 (c) 11 (d) What is the total degree of indeterminacy in the continuous prismatic beam shown in the figure below? (a) d = and k = 10 (b) d = and k = 1 (c) d = 9 and k = 10 (a) 1 (b) 2 (c) (d) 4 # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , (d) d = 9 and k = 1 mail : engineersacademy.org

7 Theory of Structures eterminacy Indeterminacy onsidering beam as axially rigid, the degree of freedom of a plane frame shown below is 49. Match List-I (Structure) with List-II (egree of static indeterminacy) and select the correct answer using the codes given below the lists : List-I () (a) 9 (b) 8 (c) 7 (d) The degree of static indeterminacy of the rigid frame having two internal hinges as shown in the figure below, is () () H I J () (a) 8 (b) 7 (c) 6 (d) The frame shown in the given figure has w/unit length (a) one unknown reaction component (b) two unknown reaction components (c) three unknown reaction components (d) six unknown reaction components List-II 1. Three 2. Six. Two 4. our odes : (a) (b) (c) (d) perfect plane frame having n number of members and j number of joints should satisfy the relation (a) n (2j ) (b) n (2j ) (c) n (2 j ) (d) n ( 2j) # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , mail : engineersacademy.org

8 8 eterminacy Indeterminacy ivil ngineering NSWRS N XLNTIONS 1. ns. (c) Reactions at =, Reactions at = 2 Reaction at = 1 Total no. of reactions = 6 No. of equilibrium equations = Where se = r equilibrium equations = 6 = s = for rigid jointed plane frames = no. of closed boxes si = 2 = 6 s = se + si = + 6 = 9 2. ns. (a) egrees of freedom of various supports (or) joints are shown in figure k = (1 + 2) = 24 (with axial deformation) = = 1 (neglecting axial deformation). ns. (d) X onsider the section XX. onsider upper part of section XX. 4. ns. (b) = (Tensile) Without the hinge at, the structure is stable and determinate. With the hinge at, static indeterminacy is negative, column will have failure. Hence the structure is unstable. 5. ns. (a) 6. ns. (d) Reactions at = Reactions at = 2 Reaction at = 1 Reactions at = 2 Total reactions (r) = 8 se = r equilibrium equations = r = 5 Si = = 2 = 6 t k a moment hinge exists. orce release at a joint moment hinge = no. of members connected to hinge 1 = 2 1 = 1 s = se + si no. of force release 7. ns. (d) = = 10 The Structure shown is unstable. Unstable Structures are called Mechanism. X # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , mail : engineersacademy.org

9 Theory of Structures eterminacy Indeterminacy 9 8. ns. (d) Se = 6 = Si = = 1 = orce = 1 = 2 orce = 2 1 = 1 9. ns. (a) S = Se + Si release = + (2 + 1) = egrees of freedom of joints are shown in figure k = 17 (with axial deformation) = 17 7 = 10 (neglecting axial deformation) k = ns. (c) egree of freedom ( k ) = No. of unknown joint displacements t pinned support O = 1 (rotation) t rigid joint of plane frame = k = = 8 (onsidering axial deformations) k = 8 no. of members (neglecting axial deformations) 14. ns. (c) = 8 = ns. (a) # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , Se = l = Si = 0 orce Releases at = 2 orce Releases at = ns. (d) S = = 0 4 Se = 6 = Si = 0 orce release at = 1 orce release at = ns. (a) S = Se + Si releases 2 = = 1 Se = 4 = 1 Si = 0 orce Release at = 1 S = = 0 t fixed support O = 0 k = = 6 (onsidering axial deformation) = 6 = (neglecting axial deformation) 15. ns. (c) Similar to question no ns. (b) Total number of reactions = = 4 quilibrium equation with lateral load only = 2 Se = xternal indeterminacy = R e equilibrium equation = 4 2 = 2 Si = Internal indeterminacy = 0 Total static indeterminacy 17. ns. (a) S = Se + Si = = 2 t, the load and member a are in the same line a = The reaction at support is vertical c = 0 mail : engineersacademy.org

10 10 eterminacy Indeterminacy ivil ngineering 18. ns. (b) k = = 6 (with axial deformation) = 6 = (neglecting axial deformation) 19. ns. (b) nalyse at joint Members and are in the same line. Hence the third force = ns. (d) S = R e + m 2j = = 0 The supports,, I will give stability to the given truss. or the central portion H No. of members m = 12 No. of joints = 9 k = 2j R e = = 12 Hence the given truss is statically determinate. s different joints have egrees of freedom it is kinematically indeterminate. 21. ns. (a) 22. ns. (b) 2. ns. (b) 24. ns. (a) 25. ns. (c) 26. ns. (d) 27. ns. (a) 28. ns. (d) Statical indeterminancy s = No. of unknown force No. of equations or plane frame, s = (m + r) n or space trus, s = (m + r) n or space frame s = (6m + r) 6n 29. ns. (c) The degree of indeterminacy Number of external reactions Number of rigid joints, S = R e + (m r r ) (j + j ) R e = = 12 j = 10 Number of joints at which releases are located, j = 1 Number of members, m = 12 s the hinge is located at a point where 4 members meet. Hence it is equivalent to three hinges. Therefore number of releases, r r =. S = 12 + ( 12 ) (10 + 1) 0. ns. (c) 1. ns. (c) 2. ns. (c). ns. (b) 4. ns. (a) 5. ns. (a) 6. ns. (b) 7. ns. (c) 8. ns. (c) 9. ns. (c) 40. ns. (c) 41. ns. (b) 42. ns. (c) 4. ns. (b) 44. ns. (b) 45. ns. (d) 46. ns. (d) 47. ns. (c) 48. ns. (d) 49. ns. (d) 50. ns. (b) = 12 + = 12 # , Ram Nagar, ambala uliya ratap Nagar, Tonk Road, Jaipur- h.: , mail : engineersacademy.org

UNIT IV FLEXIBILTY AND STIFFNESS METHOD

UNIT IV FLEXIBILTY AND STIFFNESS METHOD SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : SA-II (13A01505) Year & Sem: III-B.Tech & I-Sem Course & Branch: B.Tech