A wooden beam is loaded by a concentrated load P = 2000 N and supported by boundary conditions as shown in FigureQ5(a). The cross-section of the beam is shown in Figure Q5(b). Given that LAB = 2100 mm, LBC 2900 mm, Bo=10 mm,= 20 mm, and H = 240 mm, ho=200 mm, h₁ =20 mm, determine the following quantities below:B₁=Notes:Sign of forces and moments: We define the coordinates below in the question. We assume (1) the positive direction of avertical force points downwards; (2) the positive direction of a horizontal force points to the right; and (3) the positivedirection of a moment is anti-clockwise.Decimal points: any decimal points are fine (typically 2 decimal points) and all the numerical questions have a 10% errortolerance.Method marks: Method marks are considered using adaptive marking. The error will be carried forward, even if youranswers to the first few questions are wrong, you can still get marks if the methods for the following questions are correct.Steps are also enabled so that you will gain marks for the method. You will not lose marks no matter if your steps are corrector not.(a)PA777777YXLABB00TITTLBC(b)hiCross-sectionh₁B1Воho H2 c) Calculate the equations of internal shear force V(x) and bending moment M(x). Type the mathematical expressionsor constants, following the defined sign convection.Section AB:Internal shear force equation: V(x) =Internal bending moment equation: M(x) :Section BC:Internal shear force equation: V(x)Internal bending moment equation: M(x) ==NNN*mmN*mm

Given P = 2000N LAB =2100 mm LBC =2900 mmBo= 10 mm, B1 = 20 mm H = 240 mm h0= 200 mm h1= 20 mm

Answered: A wooden beam is loaded by a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Learning Goal: To solve for the support reactions of a frame. The frame shown in (Figure 1) is supported by a pin at A and a pin at D. The two members are connected by a pin at C. The dimensions are H₁ = 1.1 m, H₂ = 1.3 m, and L = 1 m. The applied force P = 11 kN acts at the midpoint of BC, and the distributed load has intensity w = 1.3 kN/m. Figure H1 B A P O W H₂
Please solve the below problem using FBD
3 Q2 A beam, AB, of weight W= 50 N and length L = 0.8 m is supported by two springs, as shown in figure 2.1. The two springs have identical unstressed length; the spring on the left has a spring constant, k, = 200 N/m, while the one on the right has a spring constant, k₂= 100 N/m. A vertical and downward load, P = 40 N, is applied at a distance x from A. (i) Derive the value of x for which the beam will have a horizontal orientation at equilibrium. State and justify your assumptions and comment on your working. bewalls (ii) Assume the two springs have different unstressed lengths. In your own (exham Or words, show whether it is possible for the beam to have a horizontal orientation at equilibrium when one spring is stretched while the other spring is compressed. State and justify your assumptions and comment on your working. kı k₂ (oisse of ton) 1. etgR B 10964 mtsnimsx3 to bn3 P Figure 2.1 (not to scale) A inction, and
In Figure Q4a, AC is a beam is supported at A and C with a uniformly distributed load of 40 kN/m between A and B. The distance A to B is d₁ with a length of 12.00 m; the distance B to C is d₂ with a length of 6.00 m. The point M is located at the mid-point of the beam AC. A UDL C d1 M B d2 Figure Q4a a) Draw and label the shear force diagram (SFD) for the beam shown in Figure Q4a. Label the values for shear force and bending moment at points A, B, C and at the mid-point M. [7 marks] b) Draw and label the bending moment diagram (BMD) for the beam shown in Figure Q4a and clearly indicate the type of bending that occurs between AB and between BC. On your diagram, clearly show the value of the maximum bending moment and where it occurs along the beam terms of the distance from A. In addition, label the values for bending moment at points A, B, C and at the mid-point M. [8 marks] c) The diameter (d) of a solid rod (i.e., with a circular cross-section) is 14 mm and is made from a homogeneous…
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A wooden beam is loaded by a distributed load w = 8 N/mm as shown in Figure Q4(a). The cross-section of the beam is shown in Figure Q4(b). Assume that LAB = 2100 mm, LBC = 2900 mm, W=180 mm, B%= 10 mm, and H = 230 mm, ho=30 mm. Units: use N, mm, MPa as consistent units for all calculations. Decimal points: any decimal points are fine and all the numerical questions have a 10% error tolerance. Steps: Fill the gaps in the "steps" to get some marks from the working-out process. Adaptíve marking is still used. (a) (b) hot Bo H LAB LBC Cross-section W Figure Q4: (a) A wooden beam is loaded by a distributed load, (b) cross-section of the beam.
A torsional moment T = 5,382 Nm and a load P = 55,253 N are applied at the same time to a circular hollow shaft of unknown length L, as shown in Figure Q5. The load P is offset from the centre of the circular cross-section by a distance e = 6 mm. The shaft has an inner diameter d = 43 mm and an outer diameter D = 97 mm. Point A in Figure Q5 is on the outer surface of the shaft. Figure 5 Calculate the direct (or normal) stress in the x-direction σx at point A (the 'x-direction' is along the longitudinal axis of the shaft, along its length L). Use π = 3.14159 if needed. Calculate your answer in the unit: mega-Pascal (MPa). Report you answer to 3 decimal places.
A wooden beam is loaded by a concentrated load ? = 1000 N and supported by boundary conditions as shown in Figure Q5(a). The cross-section of the beam is shown in Figure Q5(b). Given that ??? = 1600 mm, ??? = 3400 mm, ?0=10 mm, ?1 = 20 mm, and ? = 230 mm, ℎ0=150 mm, ℎ1=40 mm, determine the following quantities below:
An overhead crane can be modelled as the beam system shown in Figure Q3. The beam of length L = 2.6 m is made of steel with Young's modulus, E = 202.4 x 10⁹ N/m². The second moment of area of the beam 1 = 3.7 x 10-4 m4. The stiffness of the spring, k₁ = 6.2 x 10³ N/m. The mass due to the load being lifted, m₁ = 3.4 x 10² kg. The beam mass is negligible compared with the load. You are required to find the equivalent stiffness of the beam, and then as your answer, to find the natural frequency of the system in Hz. Fill this answer in the box below. (Express your answer to 2dp) Flg. Q3 Answer: m₁ k₁

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