A beam of length 4m and flexural stiffness (EI) of 1.4 x10 Nm², is simply supported at its ends as shown in Fig. Q3. The beam is subjected to a concentrated load of 20 kN at a distance 1m and a clockwise couple of 15 kNm applied in the plane of bending at a distance of 3m, both measured from the left end. (i) (ii) (iii) RA A 1m 20KN B 3m 15kNm I O D RD Fig. Q3: Loaded structural beam Calculate the reaction forces at the two end supports. Macaulay's approach is to be used to find slopes and deflections along the beam. Write the general expression for the bending moment at a section X-X at distance x measured from the left end to enable the solution. Using 'double integration method', derive an expression for the vertical deflection along the beam; hence determine the vertical deflection at mid-span.

A beam of length 4m and flexural stiffness (EI) of 1.4 x10 Nm², is simply supported at its ends as shown in Fig. Q3. The beam is subjected to a concentrated load of 20 kN at a distance 1m and a clockwise couple of 15 kNm applied in the plane of bending at a distance of 3m, both measured from the left end. (i) (ii) (iii) RA A 1m 20KN B 3m 15kNm I O D RD Fig. Q3: Loaded structural beam Calculate the reaction forces at the two end supports. Macaulay's approach is to be used to find slopes and deflections along the beam. Write the general expression for the bending moment at a section X-X at distance x measured from the left end to enable the solution. Using 'double integration method', derive an expression for the vertical deflection along the beam; hence determine the vertical deflection at mid-span.

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

See similar textbooks

Related questions

Q: art b) Bending moment by real forces_1 Let the origin of the horizontal coordinate x be at the…

Q: The beam W24x104 beam is constructed of A-36 steel. AC has a cross-sectional area of 1 square inch…

A: For W24×104,I=3100 in4For A-36 steel,E=210 GPa=3.046×107 lb/in2, The deflection due to the UDL of…

Q: A X w L- 12M₂ VB 2.2 What is the value of moment reaction Mg? w = 3 kN/m L = 4 m

A: Given data as per the question w =3 kN/m L =4 m

Q: An overhead crane can be modelled as the beam system shown in Figure Q3. The beam of length L = 7.2…

A: According tot he question we have L=7.2m E=183.7x109 N/m2 I=5.4x10-4 m4 k1=1.9x103 N/m m1=430kg we…

Q: 2a (c) q C M=2qa² a B A q=30kN/m 1m 0.5m | P=20kN D 1.5m (d) E q=30kN/m 1m B

A: Draw shear force and bending moment diagrams. Indicate sign and peak values of internal forces.

Q: The simply supported wooden beam shown in Fig. Q4 has a circular cross section with diameter 60 mm…

Q: A beam of uniform section is built-in at each end so as to have a clear span of 7 m. It came a…

Q: A prismatic beam of mass density p, cross-sectional area A, and length L rests upon a fixed pinned…

Q: Rigia and tw axlal Determine the internal forces and normal stresses in Bar properties bars (1) and…

A: Dear student please rate me postive :) Stay safe stay happy ! Data - given A1=720 mm2…

Q: (3) Draw the shear force diagram and bending moment diagram of the beam. Indicate the values of…

A: Given: The load at E, F = 5 kN The intensity of distributed load, w = 10 kN/m The elastic modulus…

Q: From the SFD drawn in (b), find the distance from point A to the position between points A and B…

A: For the given figure it is required to determine: (d) location of the position from A where shear…

Q: 5. The rigid beam is supported by a pin at Cand a steel wire AB (Esteel = 200 GPa). a) If the wire…

Q: on the bar at A, B and he wheel and the slid 300 N B 25

Q: A IC B 3 ft 12 ft

A: Given, loading (w)=100lb/ft To convert uniformly varying load, Area of the loading curve gives the…

Q: A steel beam ABC carries a uniformly distributed load of w (kN/m) over the unsupported length BC, as…

Q: 3.11 A beam, 12 m long, is to be simply supported at 2 m from each end and to carry a u.d.1. of 30…

A: Let 'C' be the first joint which is located at 5m left from support A.'D' be the second joint and…

Q: Problem 6 Draw the shear force and bending moment diagrams. values: a = b = 4 ft, c= d = 2 ft, P =…

A: The values are

Q: Q2(a) A simple beam is shown in Figure Q2(a) has three concentrated loads at the position indicated.…

A: Given data diameter of beam (d) = 200 mm To determine (a) support reactions (b) Maximum…

Q: A fixed beam AB, 5 m long, is carrying a point load at its centre. The moment of inertia of the beam…

A: Given that, Length of fixed beam, L=5 m,Moment of inertia of beam, I=60×106 mm4Modulus of elasticity…

Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

A beam of length 4m and flexural stiffness (EI) of 1.4 x10 Nm², is simply
supported at its ends as shown in Fig. Q3. The beam is subjected to a
concentrated load of 20 kN at a distance 1m and a clockwise couple of 15
kNm applied in the plane of bending at a distance of 3m, both measured
from the left end.
(i)
(ii)
(iii)
RA
A
1m
20KN
B
3m
15kNm I
O
D
RD
Fig. Q3: Loaded structural beam
Calculate the reaction forces at the two end supports.
Macaulay's approach is to be used to find slopes and deflections
along the beam. Write the general expression for the bending
moment at a section X-X at distance x measured from the left end
to enable the solution.
Using 'double integration method', derive an expression for the
vertical deflection along the beam; hence determine the vertical
deflection at mid-span.

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: Calculation of support reactions

VIEW

Step 2: Bending moment equation usimg Macaulay approach

VIEW

Step 3: General equation for deflection

VIEW

Step 4: Deflection at mid span

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 4 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

10 KN 8 KN 6 ΚΝ Design the beam if allowable shear stress of the beam is 1.80 MPa and allowable flexural stress is 32 MPа. 5 KN/m A C Assume that b = 150 mm and neglect the weight of the beam %3D 2.00 2.00 1.00 in meters
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
Shown below is a rigid beam ABC that is connected by pinned connections to rod (1) at A, rod (2) at C, and pivots freely at B. Rod (1) is made of bronze (E=100GPA, a=16.9x10-6/°C) and is 24mm in diameter. Rod (2) is made of aluminum (E=70GPA, a=22.5x10-6/°C) and is 16mm in diameter. The bars are unstressed as shown at 25°C. The temperature of bar (2) is reduced to 10°C while the temperature of bar (1) is held constant. Find the normal stress in bars (1) and (2). 250mm (1) |이 B A 200mm 350mm 500mm (2)
A W610 x 155 wide flange beam of length L = 4 m is suspended by two cables as shown. The unit mass of the beam is 155 kg/m. For 0= 40 deg, the tension in each cable is best given by a. 9.46 kN b. 4.73 kN c. 3.97 kN d. 0.482 kN 0 -L/2- 01 L/2-