The board that investigated the failure of the Tacoma Narrows Bridge for the Federal Works Agency printed its evidence. Among the appendices to its report of 28 March 1941 are the papers from the two months of 1938 in which Clark Eldridge’s design with twenty-five-foot trusses became Leon Moisseiff’s with eight-foot girders, and in which three separate reviews looked at the result. This piece sets them out in the order in which they were written. The words are the documents’ own, as the report gives them; the sentences between say only who wrote to whom.

July 1938: Moisseiff’s first report to Murrow

The Washington Toll Bridge Authority engaged Moisseiff as consultant on the superstructure in July 1938, after the Public Works Administration had made its offer of a grant conditional on outside consultants. His first report to Lacey V. Murrow, the Director of Highways, is headed “Preliminary Studies”. It began with the design it had been sent.

“The preliminary design made by the Highway Department of the State of Washington shows a suspension bridge of 2600 ft. main span; two side spans of 1300 ft. each; a sag of 260 ft. and stiffening trusses 22 ft. deep. The two towers were made of unequal height to suit an approaching grade on the Tacoma side of 3-1/2% and of 4-1/2% on the west shore.”

“A study of the Highway Department design was made. It was found that the stiffening trusses as shown cannot effectively stiffen the bridge except at great cost. The side spans should be shortened and the versine of the main span should be reduced.

“Assuming a truss of 1300 ft. span and 22 ft. depth with chord areas of 60 in.2 each, a live load of 500 lb. per lin. ft. would produce a deflection of approximately 43 ft. To make the side span stiffening trusses effective the size of each chord area would have to be increased from 60 in. to 140 in.2. The trusses would then sustain approximately 40% of the live load. With details and stronger web member the increase in steel of the trusses would be 1600 lbs. per ft. of bridge which would mean 4,000,000 lbs. for both side spans or, approximately, $300,000. This brings out the fact that the stiffening trusses of the side spans are of little value unless greatly increased in size.

“To approach the problem from another angle, the stiffening trusses may practically be omitted and the desired rigidity can be obtained by other means, shortening of side spans and reduction in sag ratio. It should be kept in mind that the $300,000 which would be required to strengthen the trusses in the side spans permit an increase in each cable of approximately 45 in.2.

“A study of all of the problems involved shows that it is best to attain rigidity by shortening the side spans and by a reduction of sag ratio. It is not only a better solution but also the cheapest.”

The assumptions of the comparative designs followed: a congested live load of 1,000 pounds a foot of bridge and a normal one of 700; wind of 30 pounds a square foot on the suspended span and 50 on the towers; a temperature range of forty degrees Fahrenheit either side of normal.

“The greatest downward deflection of a side span is approximately 7.5 ft. for a live load of 500 lb. per ft. of truss at highest temperature. With no stiffening trusses the same deflection becomes 8.4 ft., indicating ineffectiveness of side span stiffening trusses.

“To stiffen the bridge vertically as well as transversely the main span has been increased to 2800 ft. and the side spans reduced to 1100 ft. The increase in main span was made by moving the ‘Tacoma’ pier shoreward 200 ft.”

Of the stiffening members:

“The stiffening trusses are of silicon steel and the same for both designs. Each consists of a plate girder eight ft. deep, composed of 1 web 96 x 1/2, 4 angles 8 x 6 x 1/2 and 2 cover plates 20 x 1/2 with a gross area of 95 sq. in. The web is reinforced by longitudinal as well as vertical stiffeners on the inside face only. On the outside face vertical stiffeners will be placed at floorbeams only. This will result in a neat and pleasing appearance.”

And of the money:

“Incidentally, the difference in cable wire between the Highway design and Design B is the same as the above, the latter having additional wire in the amount of $75,000. Design B, however, has stiffening girders which are but half the weight of the original design. This is equivalent to a saving of 5,000,000 lb. or about $350,000.

“It should also be remembered that the plate girder design will command a price which will be about one cent per lb. less than for a truss.”

July 1938: the second report

Moisseiff’s second report, “Proposed Design”, priced the superstructure of the main bridge at $2,906,000 for 13,100 tons of steel, and with the approach spans at “$2,991,900, or, in round figures, $3,000,000.” It recommended a six-inch roadway slab, suspenders every fifty feet, and towers kept as low as possible “due to the relatively great effect of transverse wind pressure.”

27 July 1938: the deflections

With his computations Moisseiff sent Murrow the deflections of the bridge under the loads the design assumed.

“The greatest vertical deflections due to a live load of 1000 lb. per ft. of bridge at highest temperature are 6.0 ft. in the side spans and 10.1 ft. in the center span.

“The greatest lateral deflections due to a wind pressure of 30 lb. on the structure plus 200 lb. on the live load, are 3.4 ft. in the side spans and 20 ft. in the center span.

“The suspenders are spaced every 50 ft. and will have an approximate diameter of 1-1/8 in. and a cross section of about 0.80 sq. in. The specified ultimate strength of one rope over a sheaf of approximately 17 in. diameter will be 280,000 lb. for both parts of the rope. This will give a factor of safety of 3.3 for the normal loading of H-20 and a factor of safety of 2.2 in case one suspender should be out of order.”

31 August 1938: the Authority’s consultants

The Authority had its own Board of Consulting Engineers: Charles E. Andrew as chairman, Rear Admiral Luther E. Gregory and R. B. McMinn. Murrow asked them whether the plans were fit to go out to bid.

“In accordance with your desire, we have reviewed the plans for The Narrows Bridge to ascertain whether or not, in our opinion, they were in satisfactory shape for receipt of bids. It should be stated here that the present purpose was not to go into the Project in detail, but only in respect to major features, the intention being to make a more detailed analysis later.

“We have examined the superstructure design as to its general features. Time has not permitted the checking of stresses in the cables and stiffening trusses. In this regard we have full confidence in Mr. Moisseiff, and consider him to be among the highest authorities in suspension bridge design.

“It might seem to those who are not experienced in suspension bridge design that the proposed 2800-foot span with a distance between stiffening trusses of 39’ and a corresponding width of span ratio of 72, being without precedent, is somewhat excessive. In our opinion this feature of the design should give no concern.

“The development of the deflection theory of suspension bridge design in recent years for both vertical and lateral deflections has proven beyond doubt that the matter of width ratio is limited not by structural stress but only by the amount” of deflection that could be tolerated.

As the lenders’ engineer summarised the rest: “In a long narrow span the force of the wind is to a large extent transferred to the cables and through them to the towers. The greater the total dead load stress in the cables the more difficult it becomes to deflect them laterally and the less the side deflection of the bridge. In the proposed bridge, the dead load stress in the cables is approximately 6/7 of the total stress. We believe that the present span could be materially increased if it were necessary. In consequence we have no concern as to the general features of the proposed design of the superstructure.”

14 September 1938: Moisseiff to Condron

T. L. Condron, advisory engineer to the Reconstruction Finance Corporation, which was to buy the Authority’s bonds, had asked Moisseiff about the proportions. Moisseiff replied.

“The width of the Tacoma Narrows Bridge is 39 ft. center to center of girders. It is very narrow for the length of its center span, 2800 ft.; the ratio of width to length is 1 to 72. To obtain a reasonable degree of lateral stiffness for the bridge flatter cable curves than usual have been adopted. The versine of the cables has been made 232 ft. This is in the ratio of about 1:12.1. The increased horizontal stiffness of the cables is obtained by increasing the tension in them and thus increasing their resistance to distortion.

“The maximum horizontal deflection of the center span has been determined at 19.9 ft. which is 1:141 compared to the Golden Gate Bridge with a horizontal deflection of 27.7 ft. or 1:153 for a span of 4200 ft. For a bridge of such horizontal slenderness the obtained stiffness is rather satisfactory. I see no structural objection to the magnitude of the horizontal deflection as long as all necessary clearances have been properly provided for.

“The change in grade due to liveload is limited to 2.5%. The greatest change in grade of the Whitestone Bridge now under construction, is 2.8%.

“As the stiffening girder in a suspension bridge also acts as a horizontal wind chord it becomes of determining importance in the case of narrow bridges.

“At the middle of the center span the stress due to wind attains in the Tacoma Narrows Bridge 72% of the total stress and 62% in the Whitestone Bridge. The stiffening girder to that extent will act as a column in compression and must be proportioned and designed as such. To insure the girder acting as a column against buckling an unstiffened web plate of 2 in. thickness would be required. The necessary resistance to buckling of the web was obtained in the adopted design by stiffening the web on one side by three zees longitudinally and by two vertical stiffeners in each panel on the other side of the web. The web was then made 1/2 in. thick.”

21 September 1938: Condron’s report

Condron’s report to the Reconstruction Finance Corporation reviewed the whole project. On the superstructure he wrote:

“The super-structure of this bridge has been designed by, or under the immediate direction of Mr. Leon S. Moisseiff, C. E. and his associate Mr. Fred Lienhard, C. E., of New York City. These two engineers have a very enviable reputation as experts in the calculation of stresses and deflections of suspension bridge structures. Mr. Moisseiff has been associated as a designer with the most noteworthy suspension bridges erected in the United States, and these structures are of greater magnitude than any suspension bridges erected elsewhere in the world.

“In view of Mr. Moisseiff’s ability and reputation, I hesitate to make any criticism of the structural design, but from a practical standpoint, I would feel that the width of this Bridge relative to the length of spans was open to criticism, particularly, since it was without precedent. The Golden Gate Bridge is the longest span bridge in the world, and the width of the structure is 1/57th of the span length. That is the highest ratio of any large bridge that has been built up to date, so far as I can learn. The proposed Tacoma Narrows Bridge has a ratio of 1/72nd. I learned that certain tests had been made on models of suspension bridge spans at the University of California, and as I could find no published report of this test, I went to Berkeley and conferred with Prof. R. E. Davis particularly with reference to horizontal and vertical deflections. Prof. Davis felt reasonably confident that the lateral deflections of the Tacoma Narrows Bridge as designed and as determined by Mr. Moisseiff, would be in no way objectionable to users of the bridge.”

Having quoted Moisseiff’s letter, he went on:

“It will be noted in the above quotation that in Mr. Moisseiff’s own opinion, ‘For a bridge of such horizontal slenderness the obtained stiffness is rather satisfactory.’

“There seems to be some question even in his mind as to whether the obtained stiffness is other than rather satisfactory. The ratio of width to span is 1/72 which greatly exceeds the corresponding ratios of other long suspension bridges, which are as follows:”

“It therefore seems to me that it would be advisable to widen the super-structure to 52 ft. so as to provide for a forty-two foot roadway and two 3 ft. 3 in. sidewalks with protection curbs. This width would give a ratio of 1:54 approx. and would provide greater convenience and capacity for highway traffic. The cost would be increased considerably, but the additional cost would certainly be justified.”

His conclusion on technical soundness:

“With regard to the super-structure, I do not pretend to be qualified to analyze and check the design of the long span suspension bridge, but I have studied this design in connection with the designs of other bridges, which have been successfully erected, and are in successful operation. I also have great confidence in the ability and integrity of the Consulting Engineers under whose direction the computations and design drawings for the super-structure have been made. Moreover, these engineers have earned a very enviable reputation as experts in this field, as evidenced by the commendation from other suspension bridge experts which they have received in technical publications.

“I therefore, feel that with the exception of the unusual narrowness of this bridge with reference to its span length, the super-structure design is technically sound. It is probably technically sound notwithstanding its narrowness, but there are several reasons why it would be of material advantage if the bridge could be widened at a reasonable increase in the cost, and therefore, I recommend that serious consideration be given to the possible increase in the width of this structure, before the contract is let or work begun.”

28 September 1938: a smaller suggestion

A week later, the day after the bids were opened, Condron added a note headed “Increasing Roadway Width”.

“Assuming it is expedient to consider changing the width of the bridge as now designed, I would suggest increasing the width of the roadway from 26 ft. to 30 ft. and making the two sidewalks each 2 ft. 9 in. clear, instead of 4 ft. 9 in. clear.”

The bridge was built with a twenty-six-foot roadway and sidewalks of four feet nine inches. The Carmody board wrote of this correspondence: “Mr. Condron made no attempt to go into details of design, but commented on the flexibility of the suspended structure. However, in this respect, he deferred to the wider experience of Mr. Moisseiff.”

4 December 1940: how the agency judged a design

After the failure the board asked the Public Works Administration how it had examined the project. J. J. Madigan, Acting Commissioner of Public Works, replied to Ammann, von Kármán and Woodruff on 4 December 1940.

“Outline plans and specifications were reviewed to determine the degree of development of the project, and its indicated soundness from a technical point of view. In this connection, considerable weight was placed upon the past record of the designated architects or engineers. No attempt was made to analyze thoroughly the general or detailed design. Dependent upon the magnitude, type, location and other pertinent factors, the Engineering Division scrutinized and considered the personnel engaged by the applicant rather than the project itself. In the event it was disclosed that the project had not received adequate engineering study by recognized engineering or architectural personnel, the applicant was required to engage such technical service as would insure, beyond a reasonable doubt, the proper and sound development of the contemplated facility. I should state at this point, that, although in many instances, applicants were required to retain architectural or engineering services to supplant or supplement those earlier engaged, nevertheless in no instance did this Administration nominate, or express any preference for any particular individual, group or firm.”

“Construction plans and specifications were submitted by the applicant for review by this Administration. Again, much reliance was placed upon the architects and engineers who had been engaged by the sponsor. The review of such plans, specifications, and other contract documents was more to assure compliance with the Administration’s requirements as to hours of labor, rates of pay, open, competitive bidding, insurance, and similar administrative details than to review matters of technical design. In the event that unorthodox construction was disclosed, fundamental design principles clearly violated, poor choice of materials definitely evident, or other discrepancies were openly disclosed, the attention of the Owner was directed to such shortcomings and release of the plans for receiving bids withheld until such shortcomings were eliminated. A reasonable consideration of the wide scope of the Public Works program, involving the construction of over 16,000 projects at a cost in excess of $4,000,000,000. will indicate quite clearly that to go beyond the review indicated above was definitely impractical, would involve the expenditure of several additional millions of dollars, and afford no commensurate protection.”

“It was, and still remains, the opinion of this Administration that the above named individuals, bodies and firms were eminently qualified by training, experience, judgment and integrity to direct and supervise closely the design and construction of the bridge over the Tacoma Narrows.”

The board agreed. “Such a course has been followed generally in all large undertakings,” it wrote. “It could not have been expected that any official of the Public Works Administration should have had any doubts as to a design recommended by such engineers.”

Sources

• Othmar H. Ammann, Theodore von Kármán and Glenn B. Woodruff, The Failure of the Tacoma Narrows Bridge: A Report to the Honorable John M. Carmody, Administrator, Federal Works Agency, Pasadena, 28 March 1941: Chapter I on the approval of the design; Appendix II (Moisseiff’s reports of July 1938 and his letter of 27 July 1938); Appendix III (Madigan’s letter of 4 December 1940); Appendix IV (excerpts from Condron’s report of 21 September 1938 with his note of 28 September, Moisseiff’s letter of 14 September, and the report of the Board of Consulting Engineers of 31 August 1938). Scanned copy. authors.library.caltech.edu