Each of the three beams shown in Fig.Q3 has been provided with supportsimposing more constraints on movement than the minimum necessary toachieve static equilibrium. The built in supports prevent all lateralmovements and rotations, but do not resist longitudinal movement. Beam (a)has a simple support at the right hand end which does not move vertically.The right hand support for beam (b) prevents a change of slope but does notexert a vertical force.Each beam is made from titanium, for which Young's modulus is 106GPa andthe yield stress in 780MPa. The cross-section is square and tubular,having outside dimensions of 12mm and a wall thickness of 1.5mm. Loading.isparallel to the sides and acts through the centroid.For each beam:i. calculate the support forces and momentsii. determine an expression for the bending moment at every point in thebeam and draw the bending moment diagramiii. determine an expression for the deflection curve; draw the curve andstate the maximum valueiv. calculate the maximum longitudinal stress and the factor of safetybased on the yield stressv. state where a strain gauge should be positioned to measure the largestlongitudinal strain.(C)T20 N/mm2kN+L 100 ite 100Answer(c) (i) 3000N, 3000N, -116.7Nm, 83.3Nm (@0.1m), (ii) M=-116.7+3000x-10000x²-2000 Nm, M=-116.7Nm, (iii) v=-0.467x²+3.994x³-6.667x¹-2.667³ m, v=-1.33mm at z=100mm, (iv) 59MPa, 1.32

Answered: Each of the three beams shown in Fig.…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Each of the three beams shown in Fig.Q3 has been provided with supports
imposing more constraints on movement than the minimum necessary to
achieve static equilibrium. The built in supports prevent all lateral
movements and rotations, but do not resist longitudinal movement. Beam (a)
has a simple support at the right hand end which does not move vertically.
The right hand support for beam (b) prevents a change of slope but does not
exert a vertical force.
Each beam is made from titanium, for which Young's modulus is 106GPa and
the yield stress in 780MPa. The cross-section is square and tubular,
having outside dimensions of 12mm and a wall thickness of 1.5mm. Loading.
is
parallel to the sides and acts through the centroid.
For each beam:
i. calculate the support forces and moments
ii. determine an expression for the bending moment at every point in the
beam and draw the bending moment diagram
iii. determine an expression for the deflection curve; draw the curve and
state the maximum value
iv. calculate the maximum longitudinal stress and the factor of safety
based on the yield stress
v. state where a strain gauge should be positioned to measure the largest
longitudinal strain.
(C)
T
20 N/mm
2kN
+
L 100 ite 100
Answer
(c) (i) 3000N, 3000N, -116.7Nm, 83.3Nm (@0.1m), (ii) M=-116.7+3000x-
10000x²-2000<x-0.1> Nm, M=-116.7Nm, (iii) v=-0.467x²+3.994x³-6.667x¹-
2.667<x-0.1>³ m, v=-1.33mm at z=100mm, (iv) 59MPa, 1.32

Expert Solution

Step 1

Given:

A fixed beam with symmetrical loading on it

Required:

1. calculate the support forces and moments

ii. determine an expression for the bending moment at every point in the beam and draw the bending moment diagram

iii. determine an expression for the deflection curve; draw the curve

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