A beam AB of span 6 m is simply supported at the ends A and B and is loaded as shown in figure. If E = 200 x 106 kN/m2 and I 90 x 10-6 mt, determine by using Macaulay's method, deflection at the mid- %3D span. 8 KN/m 000 -1 m 1m- 3 m

A beam AB of span 6 m is simply supported at the ends A and B and is loaded as shown in figure. If E = 200 x 106 kN/m2 and I 90 x 10-6 mt, determine by using Macaulay's method, deflection at the mid- %3D span. 8 KN/m 000 -1 m 1m- 3 m

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.6.10P: -10 The simple beam AB shown in the figure supports two equal concentrated loads P: one acting...

See similar textbooks

Related questions

Q: Problem 1 For the beam in the figure below, assume E = 29,000 ksi and I = 600 in“ for the whole…

A: Since we only answer up to 3 subparts, we will answer the first 3. Please resubmit the question by…

Q: An overhanging beam ABC has a guidedsupport at A, a rectangular cross section, and supportsan upward…

Q: A beam ABCDE has simple supports at B and D and symmetrical overhangs at each end (see figure). The…

Q: For the beam in the figure that has as data: P = 24 kN, w = 12 kN /m and L = 8 m, El = cte. Applying…

A: According to the given details in the question. P = 24kN , E = 200 GPa = 200x106 kN/m2 , I = 5x108…

Q: A machine of mass m 500 kg is mounted on a simply supported steel beam of I 2 m having rectangular…

A: For solution refer below images.

Q: . Figure shows a simply supported beam of span 5m carrying two point loads. Find a). The deflection…

Q: A beam ABCDE has simple supports at B and D and symmetrical overhangs at each end (see figure). The…

A: Given that ,

Q: 3. A beam is loaded as shown in the figure. Use Three-Moment Equation Method. 60 kN/m C hinge 5 m 3…

A: Given dataUnifomly distributed load UDl = 60kN/mTo determine1]The reaction at the support C2]Compute…

Q: Determine the equation of the elastic curve for the cantilevered beam shown in the figure by using…

Q: 2. The simply supported beam shown in the figure consists of a W410x60 structural steel wide-flange…

A: A moment is a movement of the body when a body is rotating on an axis. The moment is also known as…

Q: the beam are as follows: IPN 280 section, L = 3.5 m, P = 18 kN, and a = 26.57°. (Note: See Table E-2…

Q: Problem 3 For the beam shown in the figure, a) Derive the equation of the elastic curve. b) Compute…

Q: Q5: A steel beam of length 7m is built in at both ends. It has a depth of 500mm and the second…

Q: 1. A semi-infinite steel beam of second moment of area I, = 4.0 × 10° mmª is supported on an elastic…

A: Write the given information.

Q: The cantilever beam consists of a rectangular structural steel tube shape [E = 27000 ksi; / = 450…

Q: A simple beam AB of length L supports aconcentrated load P at the midpoint (see gure).(a) Evaluate…

A: Given data as per question The load applied =P Calculations ∑Fx=0HA=0∑Fy=0RA+RB=P…

Q: Derive the equation of the deflection curvefor a cantilever beam AB when a couple M0…

A: Given data as per question The moment applied at point B =M0 Length of cantilever =L Calculations…

Q: Quiz: A straight beam ABCD is rigidly built-in at A and D and carries point loads of 5 kN at B and…

A: A built-in beam, also known as the fixed beam is a type os support in which movement of the beam as…

Q: Q2. A simple supported beam of span 12m carries two points loads 220 KN & 135 KN at 3m & 8m from…

A: Given data, Length of the beam, L = 12 m Two point loads, P1 = 220 KN = 220×103 N at 3 m from left…

Q: Problem: Using The moment Area method, determine the slope at point C and D of the overhanging beam…

A: Section =100×200E=75GpaI=bd312=100×200312I=66,666,666.66mm

Q: A W310 x 129 I-beam, made of A36 steel, is shown in the figure. This I-beam is 4 m long and has a…

Q: b. Determine the deflection of the beam at midpoint for the beam loading system shown in the figure…

Q: Using area-moment method, determine the maximum displacement of the cantilever beam ABC which has…

A: Answer: The maximum displacement of the cantilever beam ABC: 35 mm

Q: Hw: Find te slope and deflection in the section (A-A) and the Section cB-B) for the beam Shown.…

A: Given Data: The uniform load is w= 2 kN/m. The span of the beam is L=4.5 m The value of E=205 GPa.…

Q: For the cantilever steel beam [E = 180 GPa;1= 94 x 10 mmil. use thedouble-integration method to…

Q: 4. A cantilever of length 2m carries a point le kN at its centre. If E = 10 N/mm?and I 10 area…

Q: Problem 9: Find the Slope and deflection at B and C for a cantilever beam of L subjected to a load…

Q: Beam ABC is loaded by a uniform load q andpoint load P at joint C. Using the method of…

A: Given data as per question L = 4 m, a = 2 m , q = 15 kN/m, P = 7.5 kN,E = 200 GPa, I = 70.8 X106…

Q: The flexural rigidity (EI) of a cantilever beam is assumed to be constant over the length of the…

Q: Given the direction and values of reactions at hinge and roller of the beam shown in the figure.…

Q: A cantilever beam AB of length Land uniform flexural rigidity El has a bracket AC attached to its…

Q: A cantilever beam AB with rectangular crosssections of a constant width b and varying height hx…

A: Given data: The uniformly distributed load over the beam is q The width of the beam is b Consider at…

Q: Quiz: A straight beam ABCD is rigidly built-in at A and D and carries point loads of § kN at B and…

A: Fixed end moments are the reaction moments formed in a beam member under specific load conditions…

Q: -30. Calculate the deflection at point C of a beam subjected to uniformly distributedload w = 275…

Q: Q 1. A simple supported beam of span 9m carries two points loads 210 KN & 125 KN at 2m & 6m from…

A: Given:- the span of simple supported beam=9m Uniform distribution load throughout the beam…

Q: The steel (E 200 GPå, I = 351 x 10° mm*) beam shown below has a pin support at A, a roller support…

A: RA+RC=55×10=550 KWM=-(55×10×5)+(RC×7.2)=0Rc×7.2=2750RC=382 KN

Q: For The beam shown in The Figure belw. find deflection at point B FI =12000 KN wm? P= 50 KN M225KN.m…

Q: P B C |A LAB LBC

A: FBD: Ay= Reaction force at AMA=reaction moment at AConvert the loading condition by this (fig 2)From…

Q: 9.5-2 A simply supported beam (E = 12 GPa) car- THes a uniformly distributed load q point load P =…

Q: Obtain the equation of the deflection curve for the simple supported beam AB (see figure). Also,…

Q: A steel beam type W 250x80 is subjected to a concentrated force of 100kN at B as shown in the…

Q: h F The beam of length 5.9 (m) and cross section base 0.10 (m) and height 0.16 (m) shown is made of…

Q: Find the deflection at the mid-point BC of the loaded beam as shown in the figure by the double…

Q: Refer to the previous problem. Calculate the resulting maximum positive moment (kN-m). O 77.4 O 96.8…

Q: A beam ABC having flexural rigidityEI = 75 kN.m2 is loaded by a force P =800 N atend C and tied down…

A: Given Load, P= 800 N Length, L = 1.25 m EA = 900 kN Find Deflection at point C

Q: bläi 4 For a beam, as shown in the below figure, the deflection at the free end are 8 kN 6kN/m A_c!…

A: A free-body diagram of the above beam is given as, On using force equilibrium in a vertical…

Q: he cantilever beam shown in the figure consists of a rectangular structural steel tube shape [E =…

A: Given: The elastic modulus, E = 200 GPa The moment of inertia, I = 95 × 10^6 mm^4 The intensity of…

Q: Compound beam ABC is loaded by pointload P 51.5 kips at distance 2a/3 from point A anda triangularly…

A: given; lets take reaction force at A=RAlets take reaction force at…

Q: For the simply supported steel beam [E = 200 GPa: I = 129 x 106 mm²] shown in the figure, use the…

Q: A cantilever beam of length 100-in carries three loads P1, P2 and 15 kip as shown. Choose distances…

Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

100%

A beam AB of span 6 m is simply supported at the
ends A and B and is loaded as shown in figure. If E
200 x 106 kN/m2 and I 90 x 10-6 mt, determine
by using Macaulay's method, deflection at the mid-
%3D
span.
8 kN/m
C
D
B
000
1m 1 m
3 m

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

A simple beam AB of length L and height h (see figure) is heated in such a manner that the temperature difference 7= T{between the bottom and top of the beam is proportional to the distance from support A: that is, assume the temperature difference varies linearly along the beam: T2- Tt= Tax in which 7"0 is a constant having units of temperature (degrees) per unit distance. Determine the maximum deflection SW9Xof the beam, Repeat for a quadratic temperature variation along the beam, so T2+T1= Tax
A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable deflect ion at point C is 0.5 mm, select the lightest W360 section from Table F-l{b) that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the beam.
An object of weight Wis dropped onto the midpoint of a simple beam AB from a height h (see figure). The beam has a rectangular cross section of area A. Assuming that h is very large compared to the deflection of the beam when the weight PFis applied statically, obtain a formula for the maximum bending stress crniilx in the beam due to the falling weight.
A symmetric beam A BCD with overhangs at both ends supports a uniform load of intensity q (see figure). Determine the deflection SDat the end of the overhang. (Obtain the solution by using the modified form of Castiglianos theorem.)
A beam ABCD consisting of a simple span BD and an overhang AB\s loaded by a force P acting at the end of the bracket CEF (see figure), Determine the deflection at the end of the over h a tig. Under what conditions is this deflection upward? Under what conditions is it downward?
An S6 × 12.5 steel cantilever beam AB is supported by a steel tic rod at B as shown. The tie rod is just taut when a roller support is added at Cat a distance s to the left of £, then the distributed load q is applied to beam segment AC, Assume E = 30 × 106 psi and neglect the self-weight of the beam and tie rod. Sec Table F-2(a) in Appendix F for the properties of the S-shape beam. (a) What value of uniform load q will, if exceeded, result in buckling of the tie rod if L1, =6 ft, s = 2 ft, H = 3 ft, and d = 0.25 in.? (b) What minimum beam moment of inertia ibis required to prevent buckling of the tie rod if q = 200 lb/ft, L1, = 6 ft, H = 3 ft, d = 0.25 in., and s = 2 ft? (c) For what distance s will the tic rod be just on the verge of buckling if q = 200 lb/ft, L1= 6 ft, M = 3 ft, and d = 0.25 in.?
An overhanging beam ABC is subjected to a couple MAat the free end (see figure). The lengths of the overhang and the main span are a and L, respectively. Determine the angle of rotation 04and deflection S4at end A. (Obtain the solution by using the modified form of Castigliano's theorem.)
A cantilever beam JA of length Land height/; (see figure) is subjected to a temperature change such that the temperature at the top is 7[ and at the bottom is 7. Determine the equation of the deflection curve of the beam, the angle of rotation BBat end and the deflection 8Bat end B,
The cantilever beam ACE shown in the figure has FlexuraI rigidity EI = 2,1 x 106kip-in". Calculate the downward deflections Scand 8Sat points C and B, respectively, due to the simultaneous action of the moment of 35 kip-in. applied at point C and the concentrated load of 2,5 kips applied at the free end B.
Determine the plastic modulus Z and shape factor/for a W 12 x 14 wide-flange beam. Obtain the cross-sectional dimensions and section modulus of the beam from Table F-l(a) in Appendix F.
A propped cantilever steel beam is constructed from a W12 × 35 section. The beam is loaded by its self-weight with intensity q. The length of the beam is 1L5 ft. Let E = 30,000 ksi. Calculate the reactions at joints A and B. Find the location of zero moment within span AB. Calculate the maximum deflection of the beam and the rotation at joint B.
A simple beam ABC DE supports a uniform load of intensity iy (see figure). The moment of inertia in the central part of the beam (BCD) is twice the moment of inertia in the end parts (AB and DE). Find the deflection Scat the midpoint C of the beam. (Obtain the solution by using the modified form of Castigliano's theorem.)