For the simply supported steel beam [E = 200 GPa; I = 129 x 10^6 mm^4] shown in the figure use the double integration method to determine the deflection at B. AssumeL= 4.4m , P=72 kN, and w = 44 kN/m. Find the deflection at B, vB. |B C

For the simply supported steel beam [E = 200 GPa; I = 129 x 10^6 mm^4] shown in the figure use the double integration method to determine the deflection at B. AssumeL= 4.4m , P=72 kN, and w = 44 kN/m. Find the deflection at B, vB. |B C

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 9.5.1P: A simply supported beam (E = 1600 ksi) is loaded by a triangular distributed load from A to C(see...

See similar textbooks

Related questions

Q: A cantilever beam ACB supports two concentrated loads P, and P2, as shown in the following figure.…

A: Draw a diagram for the problem. Here, x is the distance of the cross-section at which the bending…

Q: 3- The cantilever beam shown below carries a distributed load of maximum intensity w= 20 kN/m,…

Q: A I-meter-long, simply supported copper beam (E= 117 GPa) carries uniformly distributed load q. The…

Q: a) A massless beam ABC of span L and con- staht nešural rigidity EI is simply supported at A and C,…

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: Since the beam AB shown in the figure is P = 60 kN, L = 3 m and E = 200 GPa, find the deflection at…

Q: A simply supported beam ABCD is subjected to a linearly distributed load, with wo = 100 N/m, two…

Q: A simply supported composite beam 3 m long carries a uniformly distributed load of intensity q=3…

Q: A prismatic bar AB with a solid circular cross section (diameter d) is loaded by a distributed…

A: (a) To find: The maximum shear stress in the bar. Formula used: The maximum shear stress in the bar…

Q: The slope at end of the point A (ii) The deflection at point C

Q: A simply supported beam hinged at A and supported at C, is carrying a distributed load and a point…

Q: A round steel bar having a cross section of 0.5 in.2 is attached at the top and is subjected to…

Q: The cantilevered beam depicted in the below fig. is subjected to a tip load P. The tip of a second…

Q: 8 em cm 1 cm 8icm 1 m 2m 1m Prob. 11.9

Q: In the figure, aluminum [E = 60 GPa] links (1) and (2) support rigid beam ABC. Link (1) has a…

A: Data given - a = 1380 mm, b = 760 mm, L₁= 2570 mm, and L₂ = 4650 mm. P = 32 kN A2 = 430 mm2 A1 =…

Q: For the simply supported steel beam [E = 200 GPa; I = 129 x 10^6 mm^4] shown in the figure use the…

A: A pin support will exert both horizontal and vertical components of a reaction. The support A is pin…

Q: Axial Loadings Consider the figure shown. A rigid beam is pinned at one end and supported by two…

A: For solution refer below images.

Q: the amount of collapse that will occur at the B point is 4mm. The diameter of

A: We will find out the deflection at B due to point load and moment and equate it with permissible…

Q: A circular beam carries a concentrated and a distributed load as shown in the figure. Determine the…

A: An overhanging beam is one in which the terminal portion of the beam extends beyond the support.…

Q: A simply supported beam is loaded as shown in the figure below. Use superposition theory to find: a)…

Q: Since the beam AB shown in the figure is P = 60 kN, L = 3 m and E = 200 GPa, find the deflection at…

Q: Q-2 For the simply supported steel beam [E = 200 GPa; I = 129 × 106 mm4 ] shown in Figure below,…

Q: Q/ For the beam shown in the figure below, find deflection and rotation at point B. EI=12000 kN.m2.…

Q: QUESTION 4 Solve the problem by the moment-area method. The beam has constant flexural rigidity EI.…

A: To find : The deflection δAand δB at point B and C . Given : The moment of inertia is I=18.1×106…

Q: P B A 21 21 1.50 m 1.50 m 1.50 m 1.50 m

A: given data; ⇒lets take reaction force at A=RA⇒lets take reaction force at…

Q: J: A beam is 10.5 m in length and loaded as shown in Figure Q4. If the deflection in the…

Q: For the figure shown below, obtain horizontal deflection at point c. Positive direction is from…

Q: When the mating moment MA and MB act on a simple beam as shown in the figure, find the position…

Q: A beam ABCD rests on simple supports at B and C. The beam has a slight initial curvature so that end…

Q: A wide-flange member (W 10 x 30) is compressed by axial loads that have a resultant P = 30 kips…

A: Given P = 30 k Modulus of elasticity = 29000 ksi Maximum deflection = 1/500 To find Lmax

Q: Consider the figure shown below. Find the deflection at the free end due to the self weight of the…

A: Given data Load(P) = 8 N Weight density per unit length (γ) = 9 N/m Length of bar (L) = 2 m…

Q: The Cantilever beam ABC in figure below (a) consist of two segment AB and 21, for segment BC.…

A: When any beam is subjected to load, the beam tends to deviate. When a beam deflects, the neutral…

Q: Consider a uniform rod of 1m length having rectangular cross section (see figure) with one end…

Q: 9.3-12Derive the equation of the deflection curve for a cantilever beam AB supporting a load P at…

Q: Q1 A cantilever beam AB of isosceles trapezoidal cross section has length L = 0.8 m, dimension bi =…

A: For solution refer below images.

Q: 9.4-7 A beam on simple supports is subjected to a parabolically distributed load of intensity q(x) =…

Q: A horizontal beam AB of 1.8-2 cross-sectional dimensions (b X h = 19 mm x 200 mm) is supported by an…

Q: A rectangular steel bar supports the two overhanging loads shown in the figure. Using superposition,…

A: Given DataF=500Nb=9mma=250mml=500mmh=35mm

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

Q: For the beam shown in the figure, find numerically the deflection at mid-span by using a central…

A: The Finite Differential Method (FDM) is one of the approaches used to analytically resolve…

Q: Calculate the beam deflection at point C. E = 206.8 GPa, In = 1.873 x 10-6 m4. Use either the double…

Q: A steel beam ABC is simply supported at Aand held by a high-strength steel wire at B (see figure).A…

A: Given Load, P = 240 lb Length, L = 50 in Find Deflection

Q: 4. A steel bar in Fig. 2 of length L= 2.0 m is compressed by axial load at the midpoint of one side…

Q: For the simply supported steel beam [E = 200 GPa; I = 129 x 10^6 mm^4] shown in the figure use the…

Q: ter of the beam must be at least how many mm so that the amount of collapse that will occur at point…

A: We will find out the deflection at B due to point load and moment and equate it with permissible…

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: For the cantilever beam shown in figure, which is acted upor varying between 10.8 N and 25.2 N. The…

Q: please answer the question

A: MAB=-400×108=-500 kN-mMBA=500 kN-mMBC=30×10212=30×10012=-250 kN-mMCB=250 kN-m

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

Concept explainers

Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

stepwise ans

For the simply supported steel beam [E = 200 GPa;I = 129 x 10^6 mm^4] shown in the figure use the
double integration method to determine the deflection at B. AssumeL=4.4m , P=72 kN, and w = 44
kN/m. Find the deflection at B, vB.
A
B

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 3 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 beam ABC with simple supports at A and B and an overhang BC supports a concentrated load P at the free end C (see figure). Determine the strain energy Ustored in the beam due to the load P. From the strain energy, find the deflection Scunder the load P. Calculate the numerical values of £/and Sc if the length L is 8 ft, the overhang length a is 3 ft, the beam is a W 10 x 12 steel wide-flange section, and the load P produces a maximum stress of 12,000 psi in the beam, (Use £ = 29 X 106 psi.)
Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses Jt(and k2^ and the beam has flexural rigidity EI. What is the downward displacement of point C, which is at the midpoint of the beam, when the moment MQis applied? Data for the structure are M0 = 7.5 kip-ft, L = 6 ft, EI = 520 kip-ft2, kx= 17 kip/ft, and As = 11 kip/ft. Repeat part (a), but remove Af0 and instead apply uniform load q over the entire beam.
-5 Calen1ate the deflections S 3a nd
A singly symmetric beam with a T-section (see figure) has cross-sectional dimensions b = 140 mm, a = 190, 8 mm, b. = 6,99 mm, and fc = 11,2 mm. Calculate the plastic modulus Z and the shape factor.
A simply supported beam (E = 1600 ksi) is loaded by a triangular distributed load from A to C(see figure). The load has a peak intensity q0= 10 lb/ ft, and the deflection is known to be 0.01 in, at point C. The length of the beam is 12 ft, and the ratio of the height to the width of the cross section is (h:b) 2:1, Find the height h; and width h of the cross section of the beam.
Compound beam ABC is loaded by point load P = 1.5 kips at distance 2aB from point A and a triangularly distributed load on segment BC with peak intensity qü= 0.5 kips/ft. If length a = 5 ft and length/) = 10 ft, find the deflection at B and rotation at A. Assume that £ = 29,000 ksi and / = 53.8 in4.
A cantilever beam has a length L = 12 ft and a rectangular cross section (b = 16 in., h = 24 in.), A linearly varying distributed load with peak intensity q0acts on the beam, (a) Find peak intensity q0if the deflection at joint B is known to be 0.18 in. Assume that modulus E = 30,000 ksi. (b) Find the location and magnitude of the maximum rotation of the beam.
A simple beam that is 18 ft long supports a uniform load of intensity q. The beam is constructed of two C8 x 11.5 sections (channel sections or C-shapes) on either side of a 4 × 8 (actual dimensions) wood beam (see the cross section shown in the figure part a). The modulus of elasticity of the steel (E; = 30,000 ksi) is 20 times that of the wood (Ew). (a) If the allowable stresses in the steel and wood are 12,000 psi and 900 psi, respectively, what is the allowable load qmax Note: Disregard the weight of the beam, and see Table F-3(a) of Appendix F for the dimensions and properties of the C-shape beam. (b) If the beam is rotated 90° to bend about its v axis (see figure part b) and uniform load q = 250 lb/ft is applied, find the maximum stresses trs and crw in the steel and wood, respectively Include the weight of the beam. (Assume weight densities of 35 lb/ft3 and 490 lb/ft3 for the wood and steel, respectively.)
A fixed-end beam AB carries point load P acting at point C. The beam has a rectangular cross section (b = 75 mm, h = 150 mm). Calculate the reactions of the beam and the displacement at point C. Assume that E = 190 GPa.
A cantilever beam model is often used to represent micro-clectrical-mechanical systems (MEMS) (sec figure}. The cantilever beam is made of polysilicon (E = 150 GPa) and is subjected to an electrostatic moment M applied at the end of the cantilever beam. 1 f dimensions arc h — 2 [im, h — 4 ^m, and L = 520 ^mt find expressions for the tip deflection and rotation of the cantilever beam in terms of moment M.
Beam ACE hangs from two springs, as shown in the figure. The springs have stiffnesses kxand k2and the beam has flex lira I rigidity EL (a) What is the downward displacement of point C, which is at the midpoint of the beam, when the moment M0 is applied? Data for the structure are as follows: M0= 10,0 kN m, L = 1.8 m, EI = 216 kN m2, Jt, = 250 kN/m, and k2= 160 kN/m, (b) Repeat part (a), but remove A/() and apply a uniform load q — 3.5 kN/m to the entire beam.
A cantileverbeam^Cßsupportstwo concentrated loads Ptand A, as shown in the figure. Calculate the deflections SBand 8Cat points B and C, respectively. Assume Px= 10 kN, P\ = 5 kN, L = 2.6 m, E = 200 GPa, and / = 20.1 x I0ft mm4.