1 Tension, Compression, And Shear 2 Axially Loaded Members 3 Torsion 4 Shear Forces And Bending Moments 5 Stresses In Beams (basic Topics) 6 Stresses In Beams (advanced Topics) 7 Analysis Of Stress And Strain 8 Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings) 9 Deflections Of Beams 10 Statically Indeterminate Beams 11 Columns Chapter9: Deflections Of Beams
Chapter Questions Section: Chapter Questions
Problem 9.2.1P: The equation of the deflection curve for a cantilever beam is v(x)=m0x22EI Describe the loading... Problem 9.2.2P: The equation of the deflection curve for a simply supported beam is v(x)=q024EI(2Lx3x4L3x) Derive... Problem 9.2.3P: -3 The deflection curve for a simple beam AB (see figure) is given by v=q0x360LEI(7L410L2x2+3x4)... Problem 9.2.4P: The deflection curve for a simple beam AB (sec figure) is given by v=q0L44EIsinxL Describe the load... Problem 9.2.5P: The deflection curve for a cantilever beam AB (sec figure) is given by... Problem 9.2.6P: The deflection curve for a cantilever beam AB (see figure) is given by... Problem 9.3.1P: A simply supported beam is loaded with a point load, as shown in the figure. The beam is a steel... Problem 9.3.2P: A I-meter-long, simply supported copper beam (E = 117 GPa) carries uniformly distributed load q. The... Problem 9.3.3P: A wide-flange beam (W 12 x 35) supports a uniform load on a simple span of length L = 14 ft (see... Problem 9.3.4P: A uniformly loaded, steel wide-flange beam with simple supports (see figure) has a downward... Problem 9.3.5P: What is the span length L of a uniformly loaded, simple beam of wide-flange cross section (see... Problem 9.3.6P: -6 Calculate the maximum deflection of a uniformly loaded simple beam if the span length L = 2.0 m,... Problem 9.3.7P: A cantilever beam with a uniform load (see figure) has a height h equal to 1/8 of the length L. The... Problem 9.3.8P: A gold-alloy microbeam attached to a silicon wafer behaves like a cantilever beam subjected to a... Problem 9.3.9P: Obtain a formula for the ratio c/maxof the deflection at the midpoint to the maximum deflection for... Problem 9.3.10P: A cantilever beam model is often used to represent micro-clectrical-mechanical systems (MEMS) (sec... Problem 9.3.11P: B cams AB and CDE are connected using rigid link DB with hinges (or moment releases) at ends D and B... Problem 9.3.12P: -12 Derive the equation of the deflection curve for a cantilever beam AB supporting a load P at the... Problem 9.3.13P: -13 Derive the equation of the deflection curve for a simple beam AB loaded by a couple M0at the... Problem 9.3.14P: -14 A cantilever beam AB supporting a triangularly distributed load of maximum intensity q0is shown... Problem 9.3.15P: A cantilever beam has a length L = 12 ft and a rectangular cross section (b = 16 in., h = 24 in.), A... Problem 9.3.16P: A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable... Problem 9.3.17P: -17 A cantilever beam AB is acted upon by a uniformly distributed moment (bending moment, not... Problem 9.3.18P: -18 The beam shown in the figure has a sliding support at A and a spring support at B, The sliding... Problem 9.3.19P: -19 Derive the equations of the deflect ion curve for a simple beam AB loaded by a couple M0acting... Problem 9.3.20P: -20 Derive the equations of the deflection curve for a cantilever beam AB carrying a uniform load of... Problem 9.3.21P: -21 Derive the equations of the deflection curve for a cantilever beam AB supporting a distributed... Problem 9.3.22P: -22 Derive the equations of the deflection curve for a simple beam AB with a distributed load of... Problem 9.3.23P: -23 The beam shown in the figure has a sliding support at A and a roller support at B. The sliding... Problem 9.4.1P: -1 Derive the equation of the deflection curve for a cantilever beam AB when a couple M0acts... Problem 9.4.2P: -2 A simple beam AB is subjected to a distrib uted load of intensity q(x) = q0sin x/L, where q0is... Problem 9.4.3P: -3 The simple beam AB shown in the figure has moments 2M0and A/0 acting at the ends. Derive the... Problem 9.4.4P: -4 A beam with a uniform load has a sliding support at one end and spring support at the other. The... Problem 9.4.5P: -5 The distributed load acting on a cantilever beam AB has an intensity q(x) given by the expression... Problem 9.4.6P: -6 A cantilever beam .4B is subjected to a parabolically valying load of intensity q(x)=q0(L2x2)/L2... Problem 9.4.7P: -7 A beam on simple supports is subjected to a parabolically distributed load of intensity q(x) =... Problem 9.4.8P: Derive the equation of the deflection curve for beam AB with sliding support at A and roller at B*... Problem 9.4.9P: -9 Derive the equations of the deflection curve for beam ABC with sliding support at A and roller... Problem 9.4.10P: -10 Derive the equations of the deflection curve for beam AB with sliding support at A and roller... Problem 9.5.1P: A simply supported beam (E = 1600 ksi) is loaded by a triangular distributed load from A to C(see... Problem 9.5.2P: A simply supported beam (E = 12 GPa) carries a uniformly distributed load q = 125 N/m, and a point... Problem 9.5.3P: Copper beam AB has circular cross section with a radius of 0.25 in. and length L = 3 ft. The beam is... Problem 9.5.4P: Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of... Problem 9.5.5P: A cantilever beam of a length L = 2.5 ft has a rectangular cross section {b = 4in,, h = Sin,) and... Problem 9.5.6P: A cantilever beam carries a trapezoidal distributed load (see figure). Let wB= 2.5 kN/m, wA=... Problem 9.5.7P: -5-7 A cantilever beam AB carries three equalaly spaced concentrated loads, as shown in the figure.... Problem 9.5.8P: A simple beam AB supports five equally spaced loads P (see figure). Determine the deflection Slat... Problem 9.5.9P: The cantilever beam AB shown in the figure has an extension BCD attached to its free end. A force P... Problem 9.5.10P: Beam ACE hangs from two springs, as shown in the figure. The springs have stiffnesses kxand k2and... Problem 9.5.11P: What must be the equation y =f(x) of the axis of the slightly curved beam AB (see figure) before the... Problem 9.5.12P: -12 Determine the angle of rotation Band deflection Bat the free end of a cantilever beam AB having... Problem 9.5.13P: The cantilever beam ACE shown in the figure has FlexuraI rigidity EI = 2,1 x 106kip-in". Calculate... Problem 9.5.14P: A cantilever beam is subjected to load P at mid-span and counterclockwise moment Mat B (see figure).... Problem 9.5.15P: Use the method of superposition to find the angles of rotation 9Aand SBat the supports, and the... Problem 9.5.16P: Repeat Problem 9,5-15 for the anti-symmetric loading shown in the figure. Problem 9.5.17P: A cantilever beam is subjected to a quadratic distributed load q{x) over the length of the beam (see... Problem 9.5.18P: A beam ABCD consisting of a simple span BD and an overhang AB\s loaded by a force P acting at the... Problem 9.5.19P: A horizontal load P acts at end C of the bracket ABC shown in the figure. Determine the deflection... Problem 9.5.20P: A beam ABC having flexural rigidity EI = 75 kN irT is loaded by a force P = 800 N at end C and tied... Problem 9.5.21P: Determine the angle of rotation 0Band deflection Problem 9.5.22P: -22 A simple beam AB supports a uniform load of intensity q acting over the middle region of the... Problem 9.5.23P: The overhanging beam A BCD supports two concentrated loads P and Q (see figure), For what ratio PIQ... Problem 9.5.24P: A thin metal strip of total weight W and length L is placed across the top of a flat table of width... Problem 9.5.25P: An overhanging beam ABC with flexural rigidity EI = 15 kip-in" is supported by a sliding support at... Problem 9.5.26P: A beam A BCD rests on simple supports at B and C (see figure). The beam has a slight initial... Problem 9.5.27P: The compound beam ABC shown in the figure has a sliding support at A and a fixed support at C. The... Problem 9.5.28P: A compound beam ABC DE (see figure) consists of two parts (ABC and CDE) connected by a hinge (i.e.,... Problem 9.5.29P: A steel beam ABC is simply supported at A and held by a high-strength steel wire at B (see figure).... Problem 9.5.30P: -30. Calculate the deflection at point C of a beam subjected to uniformly distributed load w = 275... Problem 9.5.31P: Compound beam ABC is loaded by point load P = 1.5 kips at distance 2aB from point A and a... Problem 9.5.32P: The compound beam shown in the figure consists of a cantilever beam AB (length L) that is... Problem 9.5.33P: -33 Find the horizontal deflection hand verti cal deflection vat the free end C of the frame ABC... Problem 9.5.34P: The fr a me A BCD shown in the heure is squeezed by two collinear forces P acting at points A and D.... Problem 9.5.35P: A framework A BCD is acted on by counterclockwise moment M at A (see figure). Assume that Elis... Problem 9.5.36P: A framework A BCD is acted on by force P at 2L/3 from 8(see figure). Assume that 7f/is constant.... Problem 9.5.37P: A beam ABCDE has simple supports at B and D and symmetrical overhangs at each end (see figure). The... Problem 9.5.38P: A frame ABC is loaded at point C by a force P acting at an angle öf to the horizontal (see figure).... Problem 9.5.39P: The wing of a large commercial jet is represented by a simplified prismatic cantilever beam model... Problem 9.5.40P: The wing of a small plane is represented by a simplified prismatic cantilever beam model acted on by... Problem 9.5.41P: Find an expression for required moment MA(in terms of q and L) that will result in rotation 9B= 0... Problem 9.5.42P: Find an expression for required moment MA(in terms of q and L) that will result in rotation êB= 0... Problem 9.5.43P: Find required distance d (in terms of L) so that rotation Ss= 0 is due to M and q loadings applied... Problem 9.5.44P: A cantilever beam has two triangular loads as shown in the figure. Find an expression for beam... Problem 9.6.1P: -1 A cantilever beam AB is subjected to a uniform load of intensity q acting throughout its length... Problem 9.6.2P: The load on a cantilever beam AB has a triangular distribution with maximum intensity^ (see figure).... Problem 9.6.3P: A cantilever beam AB is subjected to a concentrated load P and a couple MQacting at the free end... Problem 9.6.4P: Determine the angle of rotation BBand the deflection SBat the free end of a cantilever beam AB with... Problem 9.6.5P: -5 Calen1ate the deflections S 3a nd Problem 9.6.6P: A cantileverbeam^Cßsupportstwo concentrated loads Ptand A, as shown in the figure. Calculate the... Problem 9.6.7P: Obtain formulas for the angle of rotation 0Aat support A and the deflection SajAXat the midpoint for... Problem 9.6.8P: A simple beam AB supports two concentrated loads P at the positions shown in the figure. A support C... Problem 9.6.9P: A simple beam AB is subjected to a load in the form of a couple M0 acting at end B (see figure).... Problem 9.6.10P: -10 The simple beam AB shown in the figure supports two equal concentrated loads P: one acting... Problem 9.6.11P: A simple beam AB is subjected to couples M0and 2A0 acting as shown in the figure. Determine the... Problem 9.7.1P: The cantilever beam ACB shown in the figure has moments of inertia /, and I{in parts AC and CB,... Problem 9.7.2P: The cantilever beam ACB shown in the figure supports a uniform load of intensity q throughout its... Problem 9.7.3P: Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses Jt(and k2^ and... Problem 9.7.4P: -4 A simple beam ABCD has moment of inertia I near the supports and moment of iertia 2I in the... Problem 9.7.5P: A beam ABC has a rigid segment from A to B and a flexible segment with moment of inertia / from B to... Problem 9.7.6P: A simple beam ABC has a moment of inertia 1,5 from A to B and A from B to C (see figure). A... Problem 9.7.7P: The tapered cantilever beam AB shown in the figure has a thin-walled, hollow circular cross sections... Problem 9.7.8P: The tapered cantilever beam AB shown in the figure has a solid circular cross section. The diameters... Problem 9.7.9P: A tapered cantilever beam A B supports a concentrated load P at the free end (see figure). The cross... Problem 9.7.10P: A tapered cantilever beam AB supports a concentrated load P at the free end (see figure). The cross... Problem 9.7.11P: Repeat Problem 97-10, but now use the tapered propped cantilever tube A B with sliding support at B... Problem 9.7.12P: A simple beam ACE is constructed with square cross sections and a double taper (see figure). The... Problem 9.8.1P: A uniformly loaded simple beam AB (see figure) of a span length L and a rectangular cross section (b... Problem 9.8.2P: A simple beam AB of length L supports a concentrated load P at the midpoint (see figure). Evaluate... Problem 9.8.3P: A propped cantilever beam AB of length L and with a sliding support at A supports a uniform load of... Problem 9.8.4P: A simple beam AB of length L is subjected to loads that produce a symmetric deflection curve with... Problem 9.8.5P: A beam ABC with simple supports at A and B and an overhang BC supports a concentrated load P at the... Problem 9.8.6P: A simple beam ACB supporting a uniform load q over the first half of the beam and a couple of moment... Problem 9.8.7P: The frame shown in the figure consists of a beam ACB supported by a strut CD. The beam has length IL... Problem 9.9.1P: A simple beam AB of length L is loaded at the left-hand end by a couple of moment MQ(see figure).... Problem 9.9.2P: The simple beam shown in the figure supports a concentrated load P acting at distance a from the... Problem 9.9.3P: An overhanging beam ABC supports a concentrated load P at the end of the overhang (see figure). Span... Problem 9.9.4P: The cantilever beam shown in the figure supports a triangularly distributed load of maximum... Problem 9.9.5P: A simple beam ACB supports a uniform load of intensity q on the left-hand half of the span (see... Problem 9.9.6P: A cantilever beam ACB supports two concentrated loads P\ and P-,, as shown in the figure. Determine... Problem 9.9.7P: The cantilever beam A CB shown in the hgure is subjected to a uniform load of intensity q acting... Problem 9.9.8P: The frame A BC support s a concentrated load P at point C (see figure). Members AB and BC have... Problem 9.9.9P: A simple beam ABC DE supports a uniform load of intensity iy (see figure). The moment of inertia in... Problem 9.9.10P: An overhanging beam ABC is subjected to a couple MAat the free end (see figure). The lengths of the... Problem 9.9.11P: An overhanging beam ABC rests on a simple support at A and a spring support at B (see figure). A... Problem 9.9.12P: A symmetric beam A BCD with overhangs at both ends supports a uniform load of intensity q (see... Problem 9.10.1P: A heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see... Problem 9.10.2P: An object of weight Wis dropped onto the midpoint of a simple beam AB from a height h (see figure).... Problem 9.10.3P: A cantilever beam AB of length L = 6 It is constructed of a W 8 x 21 wide-flange section (see... Problem 9.10.4P: A weight W = 20 kN falls through a height h = 1,0 mm onto the midpoint or a simple beam of length L... Problem 9.10.5P: A weight W = 4000 lb falls through a height h = 0.5 in, onto the midpoint of a simple beam of length... Problem 9.10.6P: An overhanging beam ABC with a rectangular cross section has the dimensions shown in the figure. A... Problem 9.10.7P: A heavy flywheel rotates at an angular speed m about its axis of rotation. If the flywheel suddenly... Problem 9.11.1P: A simple beam AB of length L and height /; undergoes a temperature change such that the bottom of... Problem 9.11.2P: A cantilever beam JA of length Land height/; (see figure) is subjected to a temperature change such... Problem 9.11.3P: An overhanging beam ABC of height h has a sliding support at A and a roller at B, The beam is heated... Problem 9.11.4P: A simple beam AB of length L and height h (see figure) is heated in such a manner that the... Problem 9.11.5P: Beam AB has an elastic support kR at A, pin support at B, length L, height h (see figure), and is... Problem 9.10.2P: An object of weight Wis dropped onto the midpoint of a simple beam AB from a height h (see figure)....
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MECHANICS OF DEFORMABLE BODIES
Transcribed Image Text: Problem
Figure:
Steel
A=600 mm?
E=200 GPa
L=2 m
In the Figure shown, the rigid beam
with negligible mass was horizontal
before the load P was applied.
Determine the value of load P if the
vertical movement at P is 3 mm.
Draw the FBD and deformation
Aluminum
A=900 mm?
E=70 GPa
L=1.5 m
diagram.
-1.5 m
1 m
0.5 m
Branch of science that deals with the stationary and moving bodies under the influence of forces.
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