Test 23 - Shear Centre

Question 1 ప్రశ్న 1

Which statement best defines the shear centre of a beam cross-section?

A It is the point through which an axial load must pass to produce uniform normal stress. B It is the point through which the resultant transverse shear force must act so that bending occurs without twisting of the section. C It is always the point at which the bending stress is maximum. D It is the point at which the total shear stress is necessarily zero.

Question 2 ప్రశ్న 2

For a homogeneous thin-walled open section, which statement correctly distinguishes the centroid from the shear centre?

A The centroid governs torsional loading, whereas the shear centre governs only axial stress. B The centroid and shear centre must coincide for every homogeneous section. C The centroid is determined from area distribution, whereas the shear centre is the point for transverse loading without twist and the two need not coincide. D The centroid depends on Young's modulus while the shear centre depends only on density.

Question 3 ప్రశ్న 3

A thin-walled open section possesses exactly one axis of symmetry. What can be stated about its shear centre?

A It must lie somewhere on that axis of symmetry. B It must coincide with the centroid. C It must lie within the material of the section. D It must lie on an axis perpendicular to the symmetry axis through the centroid.

Question 4 ప్రశ్న 4

A homogeneous cross-section has two perpendicular axes of symmetry. Where is its shear centre located under the usual elementary beam assumptions?

A At an arbitrary point on either symmetry axis B At the extreme fibre carrying maximum shear stress C Outside the section on the major symmetry axis D At the intersection of the two symmetry axes, coinciding with the centroid

Question 5 ప్రశ్న 5

Consider a conventional thin-walled channel section with a vertical web and equal horizontal flanges projecting to the right, so that its horizontal centroidal axis is an axis of symmetry. Where is the shear centre for vertical transverse shear?

A At the centroid inside the channel B On the horizontal symmetry axis outside the section, on the side of the web opposite to the flanges C At the free end of either flange D At the mid-depth point of the web regardless of flange dimensions

Question 6 ప్రశ్న 6

An ideal thin-walled angle consists of two straight narrow legs meeting at right angles, with corner radius neglected. Where is its shear centre in the standard thin-wall idealization?

A At the centroid of the angle B At the midpoint of the longer leg C At the intersection of the centre-lines of the two legs D At a point equidistant from the two free edges

Question 7 ప్రశ్న 7

An ideal thin-walled T-section consists of a horizontal flange and a vertical stem, both represented by narrow rectangles, and is symmetric about the vertical stem centre-line. Where is its shear centre in this idealization?

A At the intersection of the flange and stem centre-lines B At the centroid regardless of flange-to-stem proportions C At the free end of the stem D Outside the section on the flange side

Question 8 ప్రశ్న 8

For a thin-walled open beam under a transverse shear force V acting along a principal bending direction, which relation correctly connects shear flow q, first moment of area Q, second moment of area I and wall thickness t?

A q = VIt/Q and τ = qI B q = Vt/(IQ) and τ = qt C q = VI/Q and τ = t/q D q = VQ/I and τ = q/t

Question 9 ప్రశ్న 9

What are the dimensions of shear flow q in a thin-walled beam?

A Force per unit area B Force per unit length C Moment per unit length D Dimensionless

Question 10 ప్రశ్న 10

For an open thin-walled section with no externally applied longitudinal edge traction, what is the shear flow at a free edge?

A It is zero at the free edge. B It is necessarily equal to V/t. C It is always maximum at the free edge. D It equals the average shear stress multiplied by the full section width.

Question 11 ప్రశ్న 11

A transverse shear force V acts at an eccentricity e from the shear centre of a beam section. What is the magnitude of the additional twisting moment about the longitudinal axis?

A V/e B Ve² C Ve D V²e

Question 12 ప్రశ్న 12

A transverse force passes exactly through the shear centre of a thin-walled open beam section. Which statement is correct?

A Both bending moment and shear stress must vanish. B The beam can carry only pure torsion. C The centroid must move to the shear centre. D The load can produce bending and shear deformation, but it produces no twisting moment due to transverse-load eccentricity.

Question 13 ప్రశ్న 13

A thin-walled channel has flange length b measured from the web centre-line, distance h between flange centre-lines, flange thickness tf and web thickness tw. Using the usual thin-wall approximation, which expression gives the distance e of the shear centre from the web centre-line on the side opposite the flanges?

A e = bhtf/(tw + tf) B e = 3b²tf/(htw + 6btf) C e = h²tw/(6b + h) D e = b²tw/(3h + 2b)

Question 14 ప్రశ్న 14

A uniform-thickness thin-walled channel has flanges of length b = 100 mm measured from the web centre-line and a distance h = 150 mm between flange centre-lines. Using e = 3b²/(h + 6b), what is the shear-centre distance from the web centre-line?

A 25 mm B 30 mm C 40 mm D 60 mm

Question 15 ప్రశ్న 15

A thin-walled channel has flange length b = 100 mm from the web centre-line, flange-centre-line spacing h = 200 mm, flange thickness tf = 5 mm and web thickness tw = 10 mm. Using e = 3b²tf/(htw + 6btf), what is e?

A 30 mm B 20 mm C 40 mm D 50 mm

Question 16 ప్రశ్న 16

A thin-walled channel has flange length b = 130 mm measured to the web centre-line, flange-centre-line spacing h = 250 mm, flange thickness tf = 3 mm and second moment of area about the horizontal symmetry axis I = 1.6096 × 10^7 mm^4. Using e = h²tfb²/(4I), what is the shear-centre distance from the web centre-line approximately?

A 27.9 mm B 38.0 mm C 40.0 mm D 49.2 mm

Question 17 ప్రశ్న 17

A uniform thin-walled channel has b = 100 mm, h = 150 mm, thickness t = 4 mm and I = 5.625 × 10^6 mm^4 about its horizontal symmetry axis. A vertical shear V = 20 kN acts through the shear centre. Using F = Vthb²/(4I) for the horizontal resultant in each flange, which pair is correct?

A F = 2.667 kN in each flange and e = 20 mm B F = 5.333 kN in each flange and e = 40 mm C F = 8.000 kN in each flange and e = 60 mm D F = 10.667 kN in each flange and e = 80 mm

Question 18 ప్రశ్న 18

For the uniform channel in the previous question, the thin-wall centroid lies 28.57 mm from the web centre-line toward the flanges, while the shear centre lies 40 mm from the web centre-line on the opposite side. If a vertical shear force of 20 kN acts through the centroid, what twisting moment about the shear centre is produced approximately?

A 0.571 kN·m B 0.800 kN·m C 1.371 kN·m D 2.000 kN·m

Question 19 ప్రశ్న 19

A uniform thin-walled channel has b = 80 mm, h = 240 mm, thickness t = 6 mm and I = 20.736 × 10^6 mm^4 about its horizontal symmetry axis. Under a vertical shear V = 30 kN, what are the flange shear flow and shear stress at the flange-web junction according to q = VQ/I?

A q = 83.33 N/mm and τ = 13.89 MPa B q = 41.67 N/mm and τ = 6.94 MPa C q = 166.67 N/mm and τ = 27.78 MPa D q = 30.00 N/mm and τ = 5.00 MPa

Question 20 ప్రశ్న 20

A transverse force acts at a fixed eccentricity of 25 mm from the shear centre of a homogeneous beam section. If the force magnitude is doubled without changing the section or load line, which statement is correct?

A The shear-centre position doubles and the twisting moment is unchanged. B The shear centre moves halfway toward the centroid. C Both the shear-centre location and eccentricity become zero. D The shear-centre position is unchanged, while the twisting moment doubles.

Question 21 ప్రశ్న 21

Which statement about the shear centre of a homogeneous thin-walled section is most accurate?

A Its position varies directly with the magnitude of transverse load. B Its position is primarily a cross-sectional geometric property and is independent of the applied load magnitude in linear elastic analysis. C It always depends directly on Young's modulus even for a uniform isotropic section. D It can be found from section area alone without considering shear-flow moments.

Question 22 ప్రశ్న 22

For a general thin-walled open section having no axis of symmetry, which statement is correct?

A The shear centre must coincide with the centroid. B The shear centre must lie at the midpoint of the longest wall. C The shear centre need not lie on a centroidal axis and may lie either inside or outside the physical section. D A shear centre does not exist unless the section has an axis of symmetry.

Question 23 ప్రశ్న 23

The internal shear flows in a thin-walled open section produce a resultant couple of magnitude 0.90 kN·m about a chosen reference point. A transverse shear force of 30 kN is to be positioned so that its moment balances this couple and no twist occurs. What eccentricity magnitude is required?

A 30 mm B 15 mm C 45 mm D 60 mm

Question 24 ప్రశ్న 24

Consider the following statements about shear centre:
1. If a cross-section has one axis of symmetry, its shear centre lies on that axis.
2. If a homogeneous cross-section has two axes of symmetry, its shear centre coincides with their intersection and hence with the centroid.
3. The shear centre of a conventional channel necessarily coincides with its centroid.
4. A transverse load through the centroid of a channel can cause twisting if the centroid and shear centre do not coincide.

Which statements are correct?

A 1 and 3 only B 2 and 4 only C 1, 2 and 3 only D 1, 2 and 4 only

Question 25 ప్రశ్న 25

Match each shear-centre quantity with its correct relationship or interpretation:
1. Shear flow in a thin wall
2. Local shear stress from known shear flow
3. Twisting moment from a transverse force eccentric to the shear centre
4. Uniform-thickness channel shear-centre distance from the web centre-line, with flange length b and flange-centre-line spacing h

P. q/t
Q. 3b²/(h + 6b)
R. VQ/I
S. Ve

Which matching is correct?

A 1-P, 2-R, 3-Q, 4-S B 1-R, 2-P, 3-S, 4-Q C 1-Q, 2-S, 3-P, 4-R D 1-S, 2-Q, 3-R, 4-P

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