Methods Of Structural Analysis Practice Questions

In the rigid-jointed frame shown in the figure, the distribution factor of the member $A D$ is closest to

The figure shows a propped cantilever with uniform flexural rigidity $EI$ (in $\text{N} \cdot \text{m}^2$ ) and subjected to a moment $M$ (in $\text{N} \cdot \text{m}$ ). Consider forces and displacements in the upward direction as positive. Find the upward reaction at the propped support B (in N) when this support settles by $(-\Delta )$ , given in metres.

In the frame shown in the figure (not to scale), all four members $(A B, B C, C D$ , and $A D)$ have the same length and same constant flexural rigidity. All the joints $A, B, C$ , and $D$ are rigid joints. The midpoints of $A B, B C, C D$ , and $A D$ , are denoted by $E, F, G$ , and $H$ , respectively. The frame is in unstable equilibrium under the shown forces of magnitude $P$ acting at $E$ and $G$ . Which of the following statements is/are TRUE?

Consider the linearly elastic plane frame shown in the figure. Members HF, FK and FG are welded together at joint F. Joints K, G and H are fixed supports. A counter-clockwise moment M is applied at joint F. Consider flexural rigidity EI= $10^5kN-m^2$ for each member and neglect axial deformations. If the magnitude (absolute value) of the support moment at H is 10 kN-m, the magnitude (absolute value) of the applied moment M (in kN-m) to maintain static equilibrium is ___________. (round off to the nearest integer)

Which of the following statement(s) is/are correct?

The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams UV and WX are connected with the help of the vertical linear spring with spring constant k = 20 kN/m. The fixed supports are provided at U and X. It is given that flexural rigidity $EI = 10^5 kN-m^2, P = 100 kN,$ and $a = 5 m$ . Force Q is applied at the center of beam WX such that the force in the spring VW becomes zero. The magnitude of force Q (in kN) is ________. (round off to the nearest integer)

A frame EFG is shown in the figure. All members are prismatic and have equal flexural rigidity. The member FG carries a uniformly distributed load w per unit length. Axial deformation of any member is neglected. Considering the joint F being rigid, the support reaction at G is

A propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure. The vertical reaction at support X ( in kN, in integer) is _____

A prismatic linearly elastic bar of length, L, cross-sectional area A, and made up of a material with Young's modulus E, is subjected to axial tensile force as shown in the figures. When the bar is subjected to axial tensile force $P_1\; and\; P_2$ , the strain energies stored in the bar are $U_1\; and\; U_2$ , respectively. If U is the strain energy stored in the same bar when subjected to an axial tensile force ( $P_1 + P_2$ ), the correct relationship is

The planar structure RST shown in the figure is roller-supported at S and pin-supported at R. Members RS and ST have uniform flexural rigidity (EI) and S is a rigid joint. Consider only bending deformation and neglect effects of self-weight and axial stiffening When the structure is subjected to a concentrated horizontal load P at the end T, the magnitude of rotation at the support R, is

The rigid-jointed plane frame QRS shown in the figure is subjected to a load P at the joint R. Let the axial deformations in the frame be neglected. If the support S undergoes a settlement of $\Delta =\frac{PL^3}{\beta EI}$ , the vertical reaction at the support S will become zero when $\beta$ is equal to

A portal frame shown in figure has a hinge support at joint P and a roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction. The flexural rigidity, EI, of each member is 10 $kNm^2$ . Under the applied load, the horizontal displacement (in mm, round off to 1 decimal place) of joint R would be _______

The figure shows a simply supported beam PQ of uniform flexural rigidity EI carrying two moments M and 2M. The slope at P will be

A vertical load of 10 kN acts on a hinge located at a distance of L/4 from the roller support Q of a beam of length L (see figure). The vertical reaction at support Q is

A prismatic beam P-Q-R of flexural rigidity $EI=1\times 10^{4}kNm^{2}$ is subjected to a moment of 180 kNm at Q as shown in the figure. The rotation at Q (in rad, up to two decimal places) is ______

The value of M in the beam ABC shown in the figure is such that the joint B does not rotate. The value of support reaction (in kN) at B should be equal to ______

Consider the portal frame shown in the figure and assume the modulus of elasticity $E=2.5\times 10^{4}$ MPa and the moment of inertial, $I=8\times 10^{8}\; mm^{4}$ for all the members of the frame. The rotations (in degrees, up to decimal place) at the rigid joint Q would be ___

For the beam shown below, the value of the support moment M is __________ kN-m.

Considering the symmetry of a rigid frame as shown below, the magnitude of the bending moment (in kNm) at P (preferably using the moment distributing method) is