Typically, an aircraft wing is supported by a single structural spar attached to the main fuselage at the wing root as shown. This arrangement can be idealized as a cantilever beam with a loading distribution characterizing wing pressure. In general, holes are introduced to the structural members to reduce the overall weight of the wing (observe the rib sections shown in 8). For the idealized beam arrangement (shown in the C), assume that the cross section of the spar is uniform and has a rectangular cross section (2" x 16"). The material is 2016-T6 Aluminum. If four 7" diameter holes are introduced to the beam (as shown in C, below), what is the maximum increase in normal stress? Ignore the effect of transverse shear.

Typically, an aircraft wing is supported by a single structural spar attached to the main fuselage at the wing root as shown. This arrangement can be idealized as a cantilever beam with a loading distribution characterizing wing pressure. In general, holes are introduced to the structural members to reduce the overall weight of the wing (observe the rib sections shown in 8). For the idealized beam arrangement (shown in the C), assume that the cross section of the spar is uniform and has a rectangular cross section (2" x 16"). The material is 2016-T6 Aluminum. If four 7" diameter holes are introduced to the beam (as shown in C, below), what is the maximum increase in normal stress? Ignore the effect of transverse shear.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.6.25P: A beam of square cross section (a = length of each side) is bent in the plane of a diagonal (see...

See similar textbooks

Related questions

Q: P (kN) 2 (kN/m) 1kN/m (a) m 1m

Q: Question # 1: Draw shear force and bending moment diagrams for the beam shown in Figure below.…

Q: The figure below shows the cross-section of an axisymmetric composite beam that comprises steel…

A: C=Couple Moment=1200 N-mdh=Hole diameter=5 mmtS=wall thickness of steel=15 mmtA=wall thickness of…

Q: The shape of the beam made of U profile ensures safe loading. Find the length c of the overhangs so…

Q: Problem 1 [30pts] The cross section of a rectangular beam having width b and height h is shown in…

A: Section modulus on any section is given by Z=Iy Where I=Area Moment of inertia about the axis of…

Q: AB beam three rectangular planks obtained by gluing and as shown in the figure has been loaded.…

A: Free Body Diagram of the body Now we will calculate the support reactions,As we can see…

Q: A beam with a solid homogeneous rectangular section is simply supported at A and B. A concentrated…

A: To Find : The maximum bending stress. Given : The concentric load is F=275 kN The lenght A to C is…

Q: A beam segment subjected to internal bending moments at sections A and B is shown along with a…

Q: A bent beam ABCD is held in equilibrium by a roller at A and by a pinned connection at D. The beam…

Q: SHOW THE FOLLOWING: 1. COMPUTATION OF REACTIONS 2. SHEAR AND MOMENT DIAGRAM 3. MAXIMUM BENDING…

Q: Consider the beam shown in the figure. The allowable tensile and compressive of a beam material are…

Q: dimensions in two different orientations as follows: Beam Section Orientation A (t mm x 2t mm); and…

A: Given data is

Q: A manufacturer wants to design a hydraulic floor crane that can lift an engine with a maximum weight…

A: To find moment of inertia

Q: Use Castigliano's theorem to compute vertical and horizontal displacements at the point of…

A: Given data,

Q: 1. Determine the maximum deflection d in a simply supported beam of length L carrying a uniformly…

Q: Consider a beam with boundary conditions, loading, and cross-section given below. In addition to the…

A: GIVEN: *P=5 kips=5 Kips = 22.2411 kN *M=144 k-in=16.2698 kNm TO FIND: (a) The normal (flexural)…

Q: 1. The cantilever beam in Figure 1 is fixed at A, and is loaded with a distributed load from A to B…

Q: Consider one wing aileron w/ a rectangular planform. This aileron w/ constant chord has a span of 6…

A: The vertical forces acting on the beam is RA+RB=10×6RA+RB=60 lbs⋯⋯⋯(1) Take moment about A =0…

Q: A beam with a solid homogeneous rectangular section is simply supported at A and B. A…

Q: Figure Q2 shows the cross section of a beam. The beam is simply supported over a span of 6 m and…

Q: A uniform beam is fixed at end x=0 and simply supported at x = L. Find the shape of the center line…

A: Solution: Given Data: To Find: Shape of the center line of the beam.

Q: A small balcony constructed of wood issupported by three identical cantilever beams (seefigure).…

A: Given Length, L1 = 2.1 m L2 = 2.5 m Design load, w = 5.5 kPa Find Weight of the…

Q: (a) Please compute and plot the shear force and bending moment diagrams for the beam shown below in…

Q: 3. Two beams are supported as shown in the diagram below, each 150mm x 200mm x 6 meters. Beam CD is…

A: A Cantilever Beam is a primary component that opposes twisting . A cantilever pillar is a bar that…

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: Figure 3 below shows a 16 m length of beam with a pinned support at A and roller support at C. The…

A: 1) Free body diagram of the beam and calculation of reaction forces The free body diagram of the…

Q: wL P w B C -6L-

A: Linear deviation of the longitudinal axis of the beam is known as deflection whereas angular…

Q: The figure below shows two solid homogenous rectangular beam sections with (breadth x depth)…

Question

Typically, an aircraft wing is supported by a single structural spar attached to the main fuselage at the wing root as
shown. This arrangement can be idealized as a cantilever beam with a loading distribution characterizing wing pressure.
In general, holes are introduced to the structural members to reduce the overall weight of the wing (observe the rib
sections shown in B). For the idealized beam arrangement (shown in the C), assume that the cross section of the spar is
uniform and has a rectangular cross section (2" x 16"). The material is 2016-T6 Aluminum.
If four 7" diameter holes are introduced to the beam (as shown in C, below), what is the maximum increase in normal
stress? Ignore the effect of transverse shear.
(A)
(C)
Wing Root
(Assumed Fixed)
80 lb/in
1.8'
1.8'
(B)
1.8'
9'
Wing Root
+
1.8'
W
Wing Tip
Fuel Tank
Wing Tip
(Assumed Free)

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: Write the given data and what is to find

VIEW

Step 2: Calculate the bending moment at any distance x from the free end of the cantilever:

VIEW

Step 3: Calculate the maximum bending moment value and the moment of inertia:

VIEW

Step 4: Calculate the value of the maximum normal stress when there are no holes present:

VIEW

Step 5: Calculate the value of the moment of inertia of the cross-section when there are holes present:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 9 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 pontoon bridge (see figure) is constructed of two longitudinal wood beams, known as bulks, that span between adjacent pontoons and support the transverse floor beams, which arc called chesses. For purposes of design, assume that a uniform floor load of 7.5 kPa acts over the chesses. (This load includes an allowance for the weights of the chesses and balks.) Also, assume that the chesses are 2.5 m long and that the balks are simply supported with a span of 3.0 m. The allowable bending stress in the wood is 15 MPa. If the balks have a square cross section, what is their minimum required width b^l Repeat part (a) if the balk width is 1.5 b and the balk depth is b; compare the cross-sectional areas of the two designs.
A simply supported wooden I-beam with a 12-ft span supports a distributed load of intensity q = 90 lb/ft over its length (see figure part a). The beam is constructed with a web of Douglas-fir plywood and flanges of pine glued to the web, as shown in the figure part b. The plywood is 3/8 in. thick: the flanges are 2 in, × 2 in, (actual size). The modulus of elasticity for the plywood is 1,600,000 psi and for the pine is 1,200,000 psL Calculate the maximum bending stresses in the pine flanges and in the plywood web. What is q, if allowable stresses are 1600 psi in the flanges and 1200 psi in the web?
A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1= 3 ft and d2= 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine the maximum height H if there is to be no tension in the brickwork.
Find expressions for shear force V and moment M at v = L/2 of beam AB in structure (a). Express V and M in terms of peak load intensity q0and beam length variable L. Repeat for structure (b) but find Fand M at m id-span of member BC.
A beam with a guided support and 10-ft span supports a distributed load of intensity q = 660 lb/ft over its first half (see figure part a) and a moment Mq = 300 ft-lb at joint B. The beam consists of a wood member (nominal dimensions 6 in. x 12 in. and actual dimensions 5.5 in. x 11.5 in. in cross section, as shown in the figure part b) that is reinforced by 0.25-in.-thick steel plates on top and bottom. The moduli of elasticity for the steel and wood are £s = 30 X 106 psi and £"w = 1.5 X 106 psi, respectively. Calculate the maximum bending stresses trs in the steel plates and rw in the wood member due to the applied loads. If the allowable bending stress in the steel plates is = 14,000 psi and that in the wood is (T.dV!= 900 psi, find qmiiX. (Assume that the moment at .fi, A/0, remains at 300 ft-lb.) If q = 660 lb/ft and allowable stress values in part (b) apply, what is Müm^ at B?
Two wood beams, each of rectangular cross section (3.0 in. x 4.0 in., actual dimensions), are glued together to form a solid beam with dimensions 6.0 in. x 4.0 in. (sec figure). The beam is simply supported with a span of S ft. What is the maximum moment Mmaxthat may be applied at the left support if the allowable shear stress in the glued joint is 200 psi? (Include the effects of the beams own weight, assuming that the wood weighs 35 lb/ft3.) Repeat part (a) if Mmaxis based on allowable bending stress of 2500 psi.
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 foot bridge on a hiking trail is constructed using two timber logs each having a diameter d = 0.5 m (see figure a). The bridge is simply supported and has a length L = 4 m. The top of each log is trimmed to form the walking surface (see Fig, b)LA simplified model of the bridge is shown in Fig. g. Each log must carry its own weight w = 1.2 kN/m and the weight (P = 850 N) of a person at mid-span, (see Fig. b). Determine the maximum tensile and compressive stresses in the beam (Fig, b) due to bending. If load h is unchanged, find the maximum permissible value of load ... if the allowable normal stress in tension and compression is 2.5 M Pa.
A cantilever beam AB having rectangular cross sections with varying width bxand varying height hxis subjected to a uniform load of intensity q (sec figure). If the width varies linearly with x according to the equation hx= bBxiL^ how should the height hxvary as a function of v in order to have a fully stressed beam? (Express hxin terms of the height hBat the fixed end of the beam.)
Beam ABC is fixed at support A and rests (at point B) upon the midpoint of beam DE (see part a of the figure). Thus, beam, ABC may be represented as a propped cantilever beam with an overhang BC and a linearly elastic support of stiffness k at point B (see part b of the figure). The distance from A to B is L = 10 ft, the distance from B to C is L/2 = 5 ft, and the length of beam DE is L = 10 ft. Both beams have the same flexural rigidity EI. A concentrated load P = 1700 lb acts at t lie free end of beam ABC. Determine the reactions RA, RB+ and MAfor beam ABC. Also, draw the shear-force and bending-moment diagrams for beam ABC, labeling all critical ordinates.
A beam of square cross section (a = length of each side) is bent in the plane of a diagonal (see figure). By removing a small amount of material at the top and bottom corners, as shown by the shaded triangles in the figure, you can increase the section modulus and obtain a stronger beam, even though the area of the cross section is reduced. Determine the ratio ß defining the areas that should be removed in order to obtain the strongest cross section in bending. By what percent is the section modulus increased when the areas arc removed?
A simple beam ACE is constructed with square cross sections and a double taper (see figure). The depth of the beam at the supports is dAand at the midpoint is dc= 2d 4. Each half of the beam has length L. Thus, the depth and moment of inertia / at distance x from the left-hand end are, respectively, in which IAis the moment of inertia at end A of the beam. (These equations are valid for .x between 0 and L, that is, for the left-hand half of the beam.) Obtain equations for the slope and deflection of the left-hand half of the beam due to the uniform load. From the equations in part (a), obtain formulas for the angle of rotation 94at support A and the deflection Scat the midpoint.