Review Innovations CE Review May 2022 – Steel Design 5

Situation 1. Situation 3.

A W12x78 bridge crane runaway girder is on a simple span A column carrying a total load of P is supported by two
of 6m. Assume that the crane wheel imparts a vertical load W21x101 beams as shown. Use Fy = 248 MPa. It is required
of 71 kN and a lateral load of 7 kN, applied at the top flange to determine the value of P without exceeding the
of the girder. A standard 0.4 kN/m rail will be used. allowable stress for web yielding. The provision of the
NSCP is given.
Neglect shear and deflection. Determine the following:
N1 = 600 mm, N2 = 300 mm.
Properties of W21x78:
The properties of the beam is as follows:
d = 300 mm Ix = 191.73x106 mm4 A = 19266 mm2 k = 40 mm
bf = 200 mm Iy = 35.07x106 mm4
d = 542 mm bf = 312 mm
w = 1.32 kN/m -
tw = 12.7 mm tf = 20.3 mm
71kN
Ix = 1007x106 mm4 Iy = 103.2x106 mm4

P
7 kN N2

N1
1. Bending stress about the x-axis.
2. Bending stress about the y-axis. 0.6L 0.4L
3. Interaction value. If Fbx = 0.6Fy and Fby= 0.75Fy
P
Situation 2.

Steel channels are used as purlins and are spaced at 1.2 m

on centers and simply supported on roof trusses 6 m apart.
Roof slope, lV:4H. Superimposed roof dead load, D = 720
Pa; Roof live load, L = 1000 Pa; Wind pressure, W = 1440
Pa; wind pressure coefficients: 0.2 pressure at the
windward side; 0.6 suction at the leeward side.

Properties of the channel: C 200 mm x 76 mm

NSCP: Web Yielding
Sx = 6.19 x 104 mm3 Sy = 1.38 x 104 mm3
weight = 79 N/m When the concentrated load is applied at a distance from
the member end that is greater than the depth of the
Assume all loads pass through the centroid of the section. member:

P ≤ 0.66Fy
4. Using the interaction formula, fbx/Fbx + fby/Fby,
tw(N+5k)
calculate the maximum ratio of actual to the allowable
bending stress for load combination 0.75(D+L+W) Fbx= When the concentrated load is applied at or near the
Fby= 207 MPa. member end:
5. Using the interaction formula, fbx/Fbx + fby/Fby,
R ≤ 0.66Fy
calculate the maximum ratio of actual to the allowable
tw(N+2.5k)
bending stress for load combination 0.75(D+L+W) if
sagrods are provided at midspan of the purlins. Fbx= Fby= R = concentrated load or reaction, N
207 MPa. N = length of bearing (not less than k for end reactions),
mm
k = distance from outer face of flange to web toe of fillet,
mm

Manila FB: @ReviewInnovationsOfficial Cebu FB: Excel-RI CE Review Specialist Inc. Davao FB: Review Innovations Davao Branch
 (02) 8735-9161 0919-227-9194  (032) 268-5989 0919-822 -5048  (082) 221-1121 0930-256-0998
 Review Innovations CE Review May 2022 – Steel Design 5
6. Determine the value of P without exceeding the
allowable stress for web yielding under the interior 11. Determine the maximum beam reaction based on
load. bearing on concrete wall.
7. Determine the value of P without exceeding the 12. Determine the maximum beam reaction based on
allowable stress for web yielding at support. bending of the base plates at a distance k from the
axis of the web.
Situation 4. 13. Determine the maximum beam reaction based on
web yielding stress over a distance N+2.5k.
A 370 mm x 450 mm base plate is used to transmit a load
from a W31x79 steel column to a 520 mm x 600 mm Problem for practice:
concrete pedestal.
Situation: Channel sections are used as a purlin. The top
Properties of W31x79: chords of the truss are sloped 4H to 1V. The trusses are
spaced 6 m on centers and the purlins are spaced 1.2 m on
d = 306 mm bf = 254 mm centers.
A = 10100 mm2 Fy = 248 MPa Superimposed dead load = 500 Pa Live load = 1000 Pa
For concrete: fc’ = 21MPa Wind load = 1400 Pa
Wind coefficients: Windward = + 0.2 Leeward = -0.6
According to the NSCP, the allowable bearing Properties of C200 x 76
pressure on the pedestal is 0.35fc’ when the load is applied Sx = 6.19 x 104 mm3 Sy = 1.38 x 104 mm3
to the full area of concrete support. If the base plate cover Weight, w = 79 N/m
less than the full area of the concrete support, the allowable Allowable bending stresses, Fbx = Fby = 207 MPa
bearing stress is to be determine by the following
expression: 1. Determine the computed maximum moment, Mx, due to
combination of dead load and live load in kN-m.
Fp = 0.35fc’ A2 but not exceed 0.7fc’ 2. Determine the computed maximum moment, My, due to
A1 combination of dead load and live load in kN-m.
3. Determine the computed uniform load due to dead load
where: and live load in kN/m.
A1 = bearing area 4. Determine the maximum bending stress about x-axis
A2 = maximum area of the concrete support that is due to D+L in MPa.
geometrically similar to the base plate. 5. Determine the maximum bending stress about y-axis
due to D+L in MPa.
It is suggested that the maximum moment for the base 6. Determine the computed maximum moment, Mx, due to
plate be computed at distances approximately 0.80bf and combination of dead load, live load and wind load in kN-
0.95d apart and the larger value is used to determine the m (D+L+W).
plate thickness required. The allowable bending stress for 7. Determine the computed maximum moment, My, due to
the base plate is taken as 0.75Fy. combination of dead load, live load and wind load in kN-
m (D+L+W).
8. Find the allowable bearing pressure on the concrete. 8. Interaction value for dead load and live load only.
9. What is the allowable axial load for the column without 9. Interaction value for load combination 0.75(D+L+W)
exceeding the allowable bearing stress of the concrete
pedestal? Problem 10-18
10. What is the required thickness of the base plate?
Solve again (problem 1-9) but assume the purlins have
sagrod at midspan.
Situation 5.

A W 600 x 110 beam is supported by a wall 250 mm thick

using steel bearing plates 300 mm x 200 mm x 25 mm. All
steel are A-36 with Fy = 248 MPa. Concrete Strength f’c = 24
MPa. Allowable Bearing strength of concrete is 0.35f’c.
Allowable compressive stress in the web at the toe of fillet
is 0.66Fy. Allowable bending stress of steel base plate is
0.75Fy.

Properties of W 600 x 110:

bf = 225 mm tw = 12 mm
d = 600 mm tf = 18 mm
k = 36 mm

Manila FB: @ReviewInnovationsOfficial Cebu FB: Excel-RI CE Review Specialist Inc. Davao FB: Review Innovations Davao Branch
 (02) 8735-9161 0919-227-9194  (032) 268-5989 0919-822 -5048  (082) 221-1121 0930-256-0998
 Review Innovations CE Review May 2022 – Steel Design 5

Situation: The W450 × 86 beam is supported by a concrete

wall and a 140-mm-wide bearing plate as shown. The
beam reaction is 300 kN. All steel are A36 steel with Fy =
250MPa. Concrete strength fc’ = 21 MPa.

The properties of W450 × 86 are as follows:

d = 450 mm tf = 18 mm
k = 36 mm bf = 190 mm
tw = 10 mm

Allowable bearing stress of concrete, Fp = 0.35fc’

Allowable bending stress on weak axis of plate, Fb = 0.75Fy

19. What is the required width of bearing plate “W”?

20. Using the width in Part 1, what is the required plate
thickness. Assume that the critical section in bending for
bearing plate is at distance “k” from the axis of the beam.
21. Determine the web yielding stress at the web toe of
fillet.

Situation: A 200 mm x 200 mm base plate is used to

transmit a load from a W31x79 steel column to a 600 mm x
600 mm concrete pedestal.

Properties of wide flange:

d = 180 mm bf = 170 mm
Fy = 248 MPa
For concrete: fc’ = 21MPa

Using NSCP:

22. Find the allowable bearing pressure on the concrete.

23. What is the allowable axial load for the column without
exceeding the allowable bearing stress of the concrete
pedestal?
24. What is the required thickness of the base plate? Using
the old version solution.
25. What is the required thickness of the base plate? Using
the new version solution.

Manila FB: @ReviewInnovationsOfficial Cebu FB: Excel-RI CE Review Specialist Inc. Davao FB: Review Innovations Davao Branch
 (02) 8735-9161 0919-227-9194  (032) 268-5989 0919-822 -5048  (082) 221-1121 0930-256-0998