Thin-Walled Structures

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

A cantilever beam with an unsymmetric cross-section is subjected to a transverse shear force (P) at its free end. P acts at the shear center of the beam cross-section. Which one of the following statements is TRUE about the deformation of this beam?

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

A thin-walled circular tube is made of a material whose magnitude of the ultimate strength, both in tension and compression, is 200 MPa. The mean radius of the tube is 0.2 m and the wall thickness is 0.004 m. Based on the maximum stress criteria, the maximum torque that the tube can sustain is ________ kN-m (round off to the nearest integer).

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is__ (rounded off to two decimal places).

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

The cross section of a thin-walled beam with uniform wall thickness t, shown in the figure, is subjected to a bending moment Mx = 10 Nm. If h = 1 m and t = 0.00 1 m, the magnitude of maximum normal stress in the cross section is _________N/m^2 (answer in integer).

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

The shear flow distribution in a single cell, thin-walled beam under the action of an arbitrary shear load ys applied at the shear centre S is shown in the figure. The cell has horizontal symmetry with booms marked by 1 to 4 that carry direct stresses. The shear modulus G is the same for all the walls, and the area of the cell is 135000 mm2. With respect to the point O marked in the figure, the distance to the shear centre S is ______ mm. (round off to the nearest integer)

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

Consider a thin-walled cylindrical pressure vessel made of an alloy with yield strength of 300 MPa. The vessel has end caps to contain the pressure. The ratio of radius of the vessel to its wall thickness is 100. As per the von Mises yield criterion, the internal pressure that would cause the failure of the vessel is _____ MPa. (round off to two decimal places)

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

The closed thin-walled rectangular channel shown in figure (i) is opened by introducing a sharp cut at the center of the bottom edge, as shown in figure (ii). Which one of the following statements is correct?

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

A 0.5 m long thin-walled circular shaft of radius 2 cm is to be designed for an axial load of 7.4 kN and a torque of 148 Nm applied at its tip, as shown in the figure. The allowable stress under uniaxial tension is 100 MPa. Using maximum principal stress criterion, the minimum thickness, t, of the shaft so that it does not fail is _____ mm (rounded off to the nearest integer).

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

For a thin-walled I section, the width of the two flanges as well as the web height are the same, i.e., 2b = 20 mm. Thickness is 0.6 mm. The second moment of area about a horizontal axis passing through the centroid is ______ mm4.

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

A damper with damping coefficient, c, is attached to a mass of 5 kg and spring of stiffness 5 kN/m as shown in figure. The system undergoes under-damped oscillations. If the ratio of the 3rd amplitude to the 4th amplitude of oscillations is 1.5, the value of c is ____ Ns/m (rounded off to the nearest integer).

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

A thin-walled cylindrical pressure vessel with closed ends, having mean radius $r$ and wall thickness $t$, is subjected to an internal gauge pressure $p$. Under the plane stress assumption, the ratio of the circumferential (hoop) stress $\sigma_h$ to the longitudinal stress $\sigma_l$ is:

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

Q.33 A shock moving into a stationary gas can be transformed to a stationary shock by a change in reference frame, as shown in the figure. Which of the following is/are true relating the flow properties in the two reference frames?

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

A thin-walled tube, with the cross-section shown in the figure, is subjected to a torque of $T = 1$ kN-m. The walls have uniform thickness $t = 1$ mm and shear modulus $G = 26$ GPa. Assume that the curved portion is semi-circular with radius $R = 50$ mm and straight length $L = 0.5$ m. The shear stress in the wall is _________ MPa (round off to 1 decimal place).

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

A thin-walled tube with external radius of 100 mm and wall thickness of 2 mm, is fixed at one end. It is subjected to a compressive force of 1 N acting at a point on the circumference parallel to its length. The maximum normal stress (in kPa) experienced by the structure is _____________ (accurate to two decimal places).

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

A thin-walled tube with external radius of 100 mm and wall thickness of 2 mm, is fixed at one end. It is subjected to a compressive force of 1 N acting at a point on the circumference parallel to its longitudinal axis. The maximum compressive stress (in kPa) developed in the tube is _________ (accurate to two decimal places).

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

The maximum normal stress in MN/m$^2$ for the thin-walled beam of square cross-section (side $b = 100$ mm, thickness $t = 2$ mm) under an applied bending moment of $M = 2$ kN-m is _________ (round off to the nearest integer).

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

The idealized cross section of a thin-walled wing box structure has two stringers carrying boom areas $B = 100$ mm$^2$ separated by height $h = 200$ mm and width $w = 400$ mm. If a vertical shear load $V_y = 10$ kN acts at the shear center, the shear flow (in N/mm) in the vertical webs is _________ (round off to the nearest integer).

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

There are 2 designs proposed for a shaft of length l, with a torque carrying capacity of T.Design I is a solid circular cross-section shaft of diameter30mm. Design II is a thin-walled circular shaft of average diameter 40mm. Thickness of the wall in Design II has to be determined such that maximum shear stress is the same in both the designs for the given torque T(so that same material can be used for manufacturing both the shafts). Ratio of mass of shaft using Design Ito the mass of shaft using Design II is

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

A gas cylinder (closed thin-walled cylindrical pressure vessel) of diameter 30cm and wall thickness 1mm is subjected to a design maximum internal pressure of 5bar (0.5MPa). The material used for manufacturing this cylinder has a failure stress of 260MPa. Assuming von Mises failure criterion, the factor of safety (with respect to maximum allowable stress) for this cylinder is

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

The cross-section of a long thin-walled member is as shown in the figure. When subjected to pure twist, point A

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

The stiffened cross-section of a long slender uniform structural member is idealized as shown in the figure below. The lumped areas at $A, B, C$ and $D$ have equal cross-sectional area of $3\text{ cm}^2$. The webs $AB, BC, CD$ and $DA$ are each $5\text{ mm}$ thick. The structural member is subjected to a twisting moment of $10\text{ kNm}$. The magnitudes of the shear flow in the webs, $q_{AB}, q_{BC}, q_{CD},$ and $q_{DA}$ in $\text{kN/m}$ are, respectively:

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

The idealized cross-section of a beam is compri sed of four identical booms connected by shear webs. The beam is subjected to a bending moment ܯas shown in the figure. The inclination of the neutral axis to the x-axis in degrees is

Subtopic: Torsion of Multi-Cell Thin-Walled Tubes

Velocity of an object fired directly in upward direction is given by ݐwhere ݐtime) is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

The total runs scored by four cricketers P, Q, R, and S in years 2009 and 2010 are given in the following table: Player | 2009 | 2010 P | 802 | 1008 Q | 765 | 912 R | 429 | 619 S | 501 | 701 The player with the lowest percentage increase in total runs is:

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

A student attempted to solve a quadratic equation in x twice. In the first attempt, he read the constant term incorrectly and got roots 8 and 2. In the second attempt, he read the coefficient of x incorrectly and got roots -9 and -1. The correct roots of the equation are:

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

Shear center for this section is located al -A. h/2 j. 12 1

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

The torque balance equation (Bredt-Batho formula) for this section leads to

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

The primary function of the fin in the vertical tail of an aircraft is to provide

Subtopic: Shear Flow in Open and Closed Thin-Walled Beams

A thin-walled tube of circular cross-section with mean radius $r$ and wall thickness $t$ has a central vertical web of thickness $t$ which divides it into two equal semicircular cells. Under a twisting moment $T$, the shear flow in the outer walls and central web are related by:

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

shown. A bending moment M, is acting on the cross-section. The ratio of the magnitude of normal stress in the top booms to that of the bottom boom is 1cm I Cl 2 cm 2 cm -- Area = 0.2cmª - Area = 0.1cm'

Subtopic: Torsion of Multi-Cell Thin-Walled Tubes

The torsion constant J of a thin-walled closed tube of thickness t and mean radius r is given by

Subtopic: Torsion of Multi-Cell Thin-Walled Tubes

Let F(s) = (s + 10) / [(s + 2)(s + 20)]. The partial fraction expansion of F(s) is:

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

The natural frequencies c of the fixed-free rod can then be obtained using