Tugevusõpetus I kodutöö 1 / Stength of materials I HW 1 (0)

Homework nr 1 in STRENGTH of MATERIALS I (MHE0011)
Variant
Title
A
B
Strength Analysis of a Bar Structure
8
9
Student
Student Code
Delivery Date
Teacher ’ Name
Karina Korell
164498 MVEB
16.12. 2017
Priit Põdra
The structure consists of 2 members : steel wire rope 7x7 and a circular bar made of Aluminum alloy Al Mg4.5Mn0.7. The structure is loaded by the vertical force F that is acting at the joint , connecting these components .
Calculate the minimum allowed diameter d of the aluminum bar and the maximum allowed value of the load F, assuming the relative position and mechanical properties of components (manufacturing tolerances, components’ mass, possible stress concentration and buckling should be neglected).
Wire rope nominal diameter is 10 mm and the strength is FLim = 58,3 kN. Yield strength of Aluminum alloy is 0,2 = 110 MPa.
The value of design factor is [S] = 6.
Required milestones:

Draw the sketch of the structure according to the values of A and B;

Derive the functions of both components internal forces as function of load F;

Compose the strength conditions for both components and calculate the diameter of aluminum bar (assuming that the safety factors of both components are approximately equal);

Calculate the maximum allowed value of the load F;

Calculate the values of components’ safety factors and check the adequate strength of the solution ;

Formulate the answer to the problem.
Angle of the aluminum bar according to the last digit of the student code A
Dimensions of the structure according to the last but one digit of the student code B
B
1
2
3
4
5
6
7
8
9
0
H, m
3
3,5
2,9
3,2
4
5
6
3,8
4,4
4,8
L, m
1
1,6
1,4
1,2
1,8
2
1,4
1,2
1,6
1,8

Table of contents

Table of contents 2
Problem Statement 3
Solution 4
1. Functions of both components internal forces 4
2. Composing the strength conditions for both components and calculating the diameter of aluminum bar 5
Strength conditions for wire rope: 5
Strength conditions for aluminum bar: 5
3. Calculating safety factors and checking the adequate strength of the solution 6
Final results 7

Problem Statement

Sketch of the problem
Initial data:
FLim = 58,3 kN
0,2 = 110 MPa
[S] = 6
Find minimum allowed diameter d of the aluminium bar and the maximum allowed value of the load F

Solution

1. Functions of both components internal forces

Section Method drawing
Conditions of equilibrium
Σ𝑭𝒙 = 𝟎;
Σ𝑭𝒚 = 𝟎;

2. Composing the strength conditions for both components and calculating the diameter of aluminum bar

Strength conditions for wire rope:

≤ =
is actual tensile force
is allowable tensile force
0,875F≤58,3*10^3/6
F≤11,104 kN
It would be safe for steel rope if the whole structure load is smaller or equal to 11,104kN

Strength conditions for aluminum bar:

= ≤ =
is the area of an aluminum bar which is a round bar because diameter is asked and it is found through equations:
is actual stress.
is allowable stress.
≤
 
≤18333333,33
r=
r≥ 0,00849m ~=8,49mm -> d≥16,98mm

3. Calculating safety factors and checking the adequate strength of the solution

Safety factor for aluminium bar
= = = =6,0121
Aluminium bar is safe enough because 6,01 ≥ 6 = [S]
Safety factor for wire rope
= FLim /
= 6,0004
Wire rope is safe enough because 6,00 ≥ 6 = [S]

Final results

Safe load for the structure
Minimum diameter for aluminium bar is 16,98mm
Maximum allowed value of the load F = 11,10kN

Evaluation table (to be filled by teacher)
Correctness of the answer
Explanations of methodics
Quality of illustrations
Symbols ’ clarifications
Overall tidyness
Total