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Past Year Questions: Theory of Column & Shear Centre | Solid Mechanics - Mechanical Engineering PDF Download
Q1: For a thin-walled section shown in the figure, points P, Q and R are located on the major bending axis X−X of the section. Point Q is located on the web whereas point S is located at the intersection of the web and the top flange of the section. [2024, Set-II]
Qualitatively, the shear center of the section lies at
(a) S
(b) R
(c) Q
(d) P
Ans: (b)
Position of shear centre will be at R.
Q2: Consider the cross-section of a beam made up of thin uniform elements having thickness t(t<<a) shown in the figure. The (x, y) coordinates of the points along the center-line of the cross-section are given in the figure. [2022, Set-I]
The coordinates of the shear center of this cross-section are:
(a) x = 0, y = 3a
(b) x = 2a, y = 2a
(c) x = -a, y = 2a
(d) x = -2a, y = a
Ans: (a)
Shear centre of section consisting of two intersecting narrow rectangles always lies at the intersection of centrelines of two rectangles.
Coordinate of shear centre (0, 3a).
Q3: A column of height h with a rectangular cross-section of size a x 2a has a buckling load of P. If the cross-section is changed to 0.5 a x 3a and its height changed to 1.5h, the buckling load of the redesigned column will be [2018 : 1 Mark, Set-I]
(a) P/12
(b) P/4
(c) P/2
(d) 3P/4
Ans: (a)
For new column,
Q4: Consider two axially loaded columns, namely, 1 and 2, made of a linear elastic material with Young’s modulus 2 x 105 MPa, square cross- section with side 10 mm, and length 1 m. For Column 1, one end is fixed and the other end is free. For Column 2, one end is fixed and the other end is pinned. Based on the Euler’s theory, the ratio (up to one decimal place) of the buckling load of Column 2 to the buckling load of Column 1 is _____. [2017 : 2 Marks, Set-I]
Ans:
∴ Required ratio =
Q5: In a system two connected rigid bars AC and BC are of identical length, L with pin supports at A and B. The bars are interconnected at C by a frictionless hinge. The rotation of the hinge is restrained by a rotational spring of stiffness, k. The system initially assumes a straight line configuration, ACB. Assuming both the bars as weightless, the rotation at supports, A and B, due to a transverse load, P applied at C is [2015 : 2 Marks, Set-II]
(a) PL/4k
(b) PL/2k
(c) P/4k
(d) Pk/4L
Ans: (a)
Deflection under load P= θL
Work done by force
Strain energy stored in spring
⇒ θ = PL/4k
Q6: If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown in the figure is
If a is amplitude constant for y, then [2014 : 2 Marks, Set-I]
Ans. (C)
∴ Solution of above differential equation is,
y = a sin mx + b cos mx
at = x = 0, y = 0
⇒ b = 0
at x = L, y = 0
⇒ 0 = sin mL
⇒ mL = nπ
⇒
∴
Q7: The possible location of shear centre of the channel section, shown below is, [2014 : 1 Mark, Set-I]
(a) P(b) Q
(c) P
(d) S
Ans: (a)
For no twistingV x e = H x h
⇒
Hence possible location of shear centre is P.
Q8: Two steel column P (length L and yield strength fy = 250 MPa) and Q (length 2L and yield strength fy = 500 MPa) have the same cross-section and end condition the ratio of buckling load of column P to that of column Q is [2013 : 1 Mark]
(a) 0.5
(b) 1.0
(c) 2.0
(d) 4.0
Ans: (d)
Buckling load,
∴
∴
Q9: The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to [2012 : 1 Mark]
(a) 0.5
(b) 1.0
(c) 2.0
(d) 4.0
Ans: (d)
Eulars critical load,
The document Past Year Questions: Theory of Column & Shear Centre | Solid Mechanics - Mechanical Engineering is a part of the Mechanical Engineering Course Solid Mechanics.
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FAQs on Past Year Questions: Theory of Column & Shear Centre - Solid Mechanics - Mechanical Engineering
| 1. What is the theory of columns in structural engineering? |  |
Ans.The theory of columns in structural engineering refers to the study of how vertical members (columns) support loads and resist buckling. It includes understanding axial loads, lateral stability, and the material properties that affect column performance. Key concepts include Euler's buckling theory, which predicts the critical load at which a column becomes unstable, and the importance of slenderness ratio in determining a column's behavior under load.
| 2. How do you determine the shear centre of a structural section? | |
Ans.The shear centre of a structural section is the point where the application of shear forces does not cause the section to rotate. To determine the shear centre, engineers typically analyze the distribution of shear flow across the section and calculate the centroid of the shear area. This involves using the geometrical properties of the section and applying principles of static equilibrium to find the location where the resultant shear forces act.
| 3. Why is the shear centre important in design? | |
Ans.The shear centre is crucial in design because it helps prevent unwanted rotations of structural members under shear loads. If the load is applied away from the shear centre, it can induce twisting or bending moments, leading to potential structural failure. Understanding the location of the shear centre allows engineers to ensure that structures behave predictably and safely under various loading conditions.
| 4. What factors affect the load-carrying capacity of columns? | |
Ans.The load-carrying capacity of columns is influenced by several factors, including the column's material properties (such as yield strength and modulus of elasticity), its geometric properties (cross-sectional area, moment of inertia, and slenderness ratio), and the type of loading (axial, eccentric, or lateral). Additionally, boundary conditions and the presence of imperfections can also impact a column's performance under load.
| 5. What is the difference between short and slender columns? | |
Ans.Short columns are those that are relatively thick and have a low slenderness ratio, which means they primarily fail by yielding under axial loads. Slender columns, on the other hand, have a high slenderness ratio and are prone to buckling under axial loads before yielding occurs. Understanding this distinction is essential for engineers to apply the correct design equations and safety factors when analyzing column behavior.
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