DEVIL PHYSICSTHE BADDEST CLASS ON

CAMPUSIB PHYSICS

PRE-IB PHYSICS

LSN 9-7: FRACTURELSN 9-8: SPANNING A SPACE:

ARCHES AND DOMES

Objectives

Know the meaning of the terms ultimate tensile strength, ultimate compressive strength, and ultimate shear strength.

Apply given safety factors to determine a not to exceed force per unit area.

Explain how reinforced concrete and prestressed concrete are made.

Objectives

For a given situation, determine the unit area required to support a maximum allowable force with a given safety factor.

Describe how a post-and-lintel opening is made.

Explain why an arched opening can support more weight than a post-and-lintel opening.

Describe the relationship between an arch and a dome.

Ultimate Strength (F/A)

Ultimate strength is the maximum force per cross-sectional area that a material can withstand before breaking

Table 9-2 [Maximum] Tensile Strength [Maximum] Compressive Strength [Maximum] Shear Strength

Different values for each type of stress

Ultimate Strength (F/A) Ultimate strength is F/A

0

0

01

LLE

AF

AF

LLE

LAF

EL

MAX

Ultimate Strength (F/A) Ultimate strength is F/A

strainEstressLLE

AF

MAX

MAX

0

Safety Factor

If the ultimate strength is the maximum a material can withstand, you want to design a structure so that the maximum anticipated load is something less than the maximum

We do this by applying a safety factor

Safety Factor

We do this by dividing the ultimate strength by the safety factor

This allows us to find maximum force for a given cross-sectional area

Or minimum area for a given force

min

....

..

AUltStr

FSF

AFS

UltStrF

FSUltStr

AF

MAX

MAX

Making Concrete Stronger

Concrete is extremely strong in compression, but weak in tension

Reinforced concrete – embedding iron rods to increase tensile and shear strength

Pre-stressed concrete – applying a tensile stress to iron rods or mesh when the concrete is poured around them giving the concrete a pre-set tensile load which allows them to withstand a higher compressive load

Arches and Domes In a post and lintel entryway, all of

the structure’s weight above the entryway is supported by sheer stress in the lintel and compressive stress in the posts.

Arches and Domes Because an arch is

at an angle to the weight, the normal force counteracting the weight will have x- and y-components

FN

Arches and Domes The x-component

of the normal force is transmitted to the walls next to the archway.

The shear stress in both x- and y-directions are distributed over a wider cross-sectional area

FN

Arches and Domes

Therefore, an arch can support a great deal more weight than a post and lintel made of the same material and same cross-sectional area.

FN

Arches and Domes Also, the greater the height-to-width ratio, the

greater the supporting capacity because more weight is transferred to the walls and greater cross-sectional are to handle the shear stress.

Arches and Domes

A dome is an arch that is rotated 360º and provides the same support properties as an arch

Do the reading activity to gain better understanding and to appreciate the historical and architectural significance of arches and domes

LET’S DO SOME HOMEWORK PROBLEMS

Objectives

Know the meaning of the terms ultimate tensile strength, ultimate compressive strength, and ultimate shear strength.

Apply given safety factors to determine a not to exceed force per unit area.

Explain how reinforced concrete and prestressed concrete are made.

Objectives

For a given situation, determine the unit area required to support a maximum allowable force with a given safety factor.

Describe how a post-and-lintel opening is made.

Explain why an arched opening can support more weight than a post-and-lintel opening.

Describe the relationship between an arch and a dome.

QUESTIONS?

#55-62 (#63 is for brilliant students only)

Homework